Results of Jacobian Elliptic Functions
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 22.2#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = \frac{\Jacobithetaq{2}^{2}@{0}{q}}{\Jacobithetaq{3}^{2}@{0}{q}}} | k =((JacobiTheta2(0, q))^(2))/((JacobiTheta3(0, q))^(2)) |
k =Divide[(EllipticTheta[2, 0, q])^(2),(EllipticTheta[3, 0, q])^(2)] |
Failure | Failure | Error | Successful |
| 22.2#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{\prime} = \frac{\Jacobithetaq{4}^{2}@{0}{q}}{\Jacobithetaq{3}^{2}@{0}{q}}} | sqrt(1 - (k)^(2))=((JacobiTheta4(0, q))^(2))/((JacobiTheta3(0, q))^(2)) |
Sqrt[1 - (k)^(2)]=Divide[(EllipticTheta[4, 0, q])^(2),(EllipticTheta[3, 0, q])^(2)] |
Failure | Failure | Error | Successful |
| 22.2#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \frac{\pi}{2}\Jacobithetaq{3}^{2}@{0}{q}} | EllipticK(k)=(Pi)/(2)*(JacobiTheta3(0, q))^(2) |
EllipticK[(k)^2]=Divide[Pi,2]*(EllipticTheta[3, 0, q])^(2) |
Failure | Failure | Error | Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[q, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[q, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[q, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[q, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 22.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \frac{\pi z}{2\!\compellintKk@{k}}} | zeta =(Pi*z)/(2*EllipticK(k)) |
\[zeta]=Divide[Pi*z,2*EllipticK[(k)^2]] |
Failure | Failure | Error | Error |
| 22.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{k} = \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}}} | JacobiSN(z, k)=(JacobiTheta3(0, q))/(JacobiTheta2(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta4(zeta, q)) |
JacobiSN[z, (k)^2]=Divide[EllipticTheta[3, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[1, \[zeta], q],EllipticTheta[4, \[zeta], q]] |
Failure | Failure | Error | Error |
| 22.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}} = \frac{1}{\Jacobiellnsk@{z}{k}}} | (JacobiTheta3(0, q))/(JacobiTheta2(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta4(zeta, q))=(1)/(JacobiNS(z, k)) |
Divide[EllipticTheta[3, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[1, \[zeta], q],EllipticTheta[4, \[zeta], q]]=Divide[1,JacobiNS[z, (k)^2]] |
Failure | Failure | Error | Error |
| 22.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{k} = \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}}} | JacobiCN(z, k)=(JacobiTheta4(0, q))/(JacobiTheta2(0, q))*(JacobiTheta2(zeta, q))/(JacobiTheta4(zeta, q)) |
JacobiCN[z, (k)^2]=Divide[EllipticTheta[4, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[2, \[zeta], q],EllipticTheta[4, \[zeta], q]] |
Failure | Failure | Error | Error |
| 22.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}} = \frac{1}{\Jacobiellnck@{z}{k}}} | (JacobiTheta4(0, q))/(JacobiTheta2(0, q))*(JacobiTheta2(zeta, q))/(JacobiTheta4(zeta, q))=(1)/(JacobiNC(z, k)) |
Divide[EllipticTheta[4, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[2, \[zeta], q],EllipticTheta[4, \[zeta], q]]=Divide[1,JacobiNC[z, (k)^2]] |
Failure | Failure | Error | Error |
| 22.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{k} = \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{3}@{0}{q}}\frac{\Jacobithetaq{3}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}}} | JacobiDN(z, k)=(JacobiTheta4(0, q))/(JacobiTheta3(0, q))*(JacobiTheta3(zeta, q))/(JacobiTheta4(zeta, q)) |
JacobiDN[z, (k)^2]=Divide[EllipticTheta[4, 0, q],EllipticTheta[3, 0, q]]*Divide[EllipticTheta[3, \[zeta], q],EllipticTheta[4, \[zeta], q]] |
Failure | Failure | Error | Error |
| 22.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{3}@{0}{q}}\frac{\Jacobithetaq{3}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}} = \frac{1}{\Jacobiellndk@{z}{k}}} | (JacobiTheta4(0, q))/(JacobiTheta3(0, q))*(JacobiTheta3(zeta, q))/(JacobiTheta4(zeta, q))=(1)/(JacobiND(z, k)) |
Divide[EllipticTheta[4, 0, q],EllipticTheta[3, 0, q]]*Divide[EllipticTheta[3, \[zeta], q],EllipticTheta[4, \[zeta], q]]=Divide[1,JacobiND[z, (k)^2]] |
Failure | Failure | Error | Error |
| 22.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsdk@{z}{k} = \frac{\Jacobithetaq{3}^{2}@{0}{q}}{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}}} | JacobiSD(z, k)=((JacobiTheta3(0, q))^(2))/(JacobiTheta2(0, q)*JacobiTheta4(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta3(zeta, q)) |
JacobiSD[z, (k)^2]=Divide[(EllipticTheta[3, 0, q])^(2),EllipticTheta[2, 0, q]*EllipticTheta[4, 0, q]]*Divide[EllipticTheta[1, \[zeta], q],EllipticTheta[3, \[zeta], q]] |
Failure | Failure | Error | Error |
| 22.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}^{2}@{0}{q}}{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}} = \frac{1}{\Jacobielldsk@{z}{k}}} | ((JacobiTheta3(0, q))^(2))/(JacobiTheta2(0, q)*JacobiTheta4(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta3(zeta, q))=(1)/(JacobiDS(z, k)) |
Divide[(EllipticTheta[3, 0, q])^(2),EllipticTheta[2, 0, q]*EllipticTheta[4, 0, q]]*Divide[EllipticTheta[1, \[zeta], q],EllipticTheta[3, \[zeta], q]]=Divide[1,JacobiDS[z, (k)^2]] |
Failure | Failure | Error | Error |
| 22.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcdk@{z}{k} = \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}}} | JacobiCD(z, k)=(JacobiTheta3(0, q))/(JacobiTheta2(0, q))*(JacobiTheta2(zeta, q))/(JacobiTheta3(zeta, q)) |
JacobiCD[z, (k)^2]=Divide[EllipticTheta[3, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[2, \[zeta], q],EllipticTheta[3, \[zeta], q]] |
Failure | Failure | Error | Error |
| 22.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}} = \frac{1}{\Jacobielldck@{z}{k}}} | (JacobiTheta3(0, q))/(JacobiTheta2(0, q))*(JacobiTheta2(zeta, q))/(JacobiTheta3(zeta, q))=(1)/(JacobiDC(z, k)) |
Divide[EllipticTheta[3, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[2, \[zeta], q],EllipticTheta[3, \[zeta], q]]=Divide[1,JacobiDC[z, (k)^2]] |
Failure | Failure | Error | Error |
| 22.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsck@{z}{k} = \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{2}@{\zeta}{q}}} | JacobiSC(z, k)=(JacobiTheta3(0, q))/(JacobiTheta4(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta2(zeta, q)) |
JacobiSC[z, (k)^2]=Divide[EllipticTheta[3, 0, q],EllipticTheta[4, 0, q]]*Divide[EllipticTheta[1, \[zeta], q],EllipticTheta[2, \[zeta], q]] |
Failure | Failure | Error | Error |
| 22.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{2}@{\zeta}{q}} = \frac{1}{\Jacobiellcsk@{z}{k}}} | (JacobiTheta3(0, q))/(JacobiTheta4(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta2(zeta, q))=(1)/(JacobiCS(z, k)) |
Divide[EllipticTheta[3, 0, q],EllipticTheta[4, 0, q]]*Divide[EllipticTheta[1, \[zeta], q],EllipticTheta[2, \[zeta], q]]=Divide[1,JacobiCS[z, (k)^2]] |
Failure | Failure | Error | Error |
| 22.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genJacobiellk{p}{q}@{z}{k} = \frac{\genJacobiellk{p}{r}@{z}{k}}{\genJacobiellk{q}{r}@{z}{k}}} | genJacobiellk(p)*q* z*k =(genJacobiellk(p)*r* z*k)/(genJacobiellk(q)*r* z*k) |
genJacobiellk(p)*q* z*k =Divide[genJacobiellk(p)*r* z*k,genJacobiellk(q)*r* z*k] |
Failure | Failure | Error | Skip |
| 22.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\genJacobiellk{p}{r}@{z}{k}}{\genJacobiellk{q}{r}@{z}{k}} = \frac{1}{\genJacobiellk{q}{p}@{z}{k}}} | (genJacobiellk(p)*r* z*k)/(genJacobiellk(q)*r* z*k)=(1)/(genJacobiellk(q)*p* z*k) |
Divide[genJacobiellk(p)*r* z*k,genJacobiellk(q)*r* z*k]=Divide[1,genJacobiellk(q)*p* z*k] |
Failure | Failure | Error | Skip |
| 22.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genJacobiellk{p}{q}@{z}{k} = \ifrac{\Jacobithetatau{p}@{z}{\tau}}{\Jacobithetatau{q}@{z}{\tau}}} | genJacobiellk(p)*q* z*k =(JacobiThetap(z,exp(I*Pi*tau)))/(JacobiThetaq(z,exp(I*Pi*tau))) |
genJacobiellk(p)*q* z*k =Divide[EllipticTheta[p, z, \[Tau]],EllipticTheta[q, z, \[Tau]]] |
Failure | Failure | Error | Skip |
| 22.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau = \ifrac{\iunit\ccompellintKk@{k}}{\compellintKk@{k}}} | tau =(I*EllipticCK(k))/(EllipticK(k)) |
\[Tau]=Divide[I*EllipticK[1-(k)^2],EllipticK[(k)^2]] |
Failure | Failure | Error | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[k, 1], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.034924298733449, 0.929003383041147] <- {Rule[k, 2], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.1238725324006347, 0.9602938378765811] <- {Rule[k, 3], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[k, 1], Rule[τ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk^{2}@{z}{k}+\Jacobiellcnk^{2}@{z}{k} = k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k}} | (JacobiSN(z, k))^(2)+ (JacobiCN(z, k))^(2)= (k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2) |
(JacobiSN[z, (k)^2])^(2)+ (JacobiCN[z, (k)^2])^(2)= (k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2) |
Successful | Successful | - | - |
| 22.6.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k} = 1} | (k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2)= 1 |
(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2)= 1 |
Successful | Successful | - | - |
| 22.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1+\Jacobiellcsk^{2}@{z}{k} = k^{2}+\Jacobielldsk^{2}@{z}{k}} | 1 + (JacobiCS(z, k))^(2)= (k)^(2)+ (JacobiDS(z, k))^(2) |
1 + (JacobiCS[z, (k)^2])^(2)= (k)^(2)+ (JacobiDS[z, (k)^2])^(2) |
Successful | Successful | - | - |
| 22.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}+\Jacobielldsk^{2}@{z}{k} = \Jacobiellnsk^{2}@{z}{k}} | (k)^(2)+ (JacobiDS(z, k))^(2)= (JacobiNS(z, k))^(2) |
(k)^(2)+ (JacobiDS[z, (k)^2])^(2)= (JacobiNS[z, (k)^2])^(2) |
Successful | Successful | - | - |
| 22.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}+1 = \Jacobielldck^{2}@{z}{k}} | 1 - (k)^(2)* (JacobiSC(z, k))^(2)+ 1 = (JacobiDC(z, k))^(2) |
1 - (k)^(2)* (JacobiSC[z, (k)^2])^(2)+ 1 = (JacobiDC[z, (k)^2])^(2) |
Failure | Failure | Fail 5.538045195-1.298501057*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}1.632868431-.533445486*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}.8869726205+.142192957*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}5.538045195+1.298501057*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[5.538045200949385, -1.2985010548545433] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.6328684295963352, -0.5334454854262538] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8869726205411628, 0.14219295744217275] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.538045200949385, 1.2985010548545433] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldck^{2}@{z}{k} = {k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}+k^{2}} | (JacobiDC(z, k))^(2)= 1 - (k)^(2)* (JacobiNC(z, k))^(2)+ (k)^(2) |
(JacobiDC[z, (k)^2])^(2)= 1 - (k)^(2)* (JacobiNC[z, (k)^2])^(2)+ (k)^(2) |
Failure | Failure | Fail -4.538045196+1.298501057*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-.632868431+.533445486*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}.113027376-.142192958*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-4.538045196-1.298501057*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-4.5380452009493855, 1.2985010548545435] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6328684295963332, 0.5334454854262538] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.11302737945883834, -0.14219295744217342] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.5380452009493855, -1.2985010548545435] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k} = k^{2}(\Jacobiellcdk^{2}@{z}{k}-1)} | - (k)^(2)* 1 - (k)^(2)* (JacobiSD(z, k))^(2)= (k)^(2)*((JacobiCD(z, k))^(2)- 1) |
- (k)^(2)* 1 - (k)^(2)* (JacobiSD[z, (k)^2])^(2)= (k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1) |
Failure | Failure | Fail 3.538045195-1.298501057*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-.767955680e-1-.7785401828*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}.3808337301+8.838098584*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}3.538045195+1.298501057*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[3.5380452009493846, -1.2985010548545433] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.07679556965128587, -0.7785401828344382] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.3808337424857964, 8.838098611812974] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.5380452009493846, 1.2985010548545433] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}(\Jacobiellcdk^{2}@{z}{k}-1) = {k^{\prime}}^{2}(1-\Jacobiellndk^{2}@{z}{k})} | (k)^(2)*((JacobiCD(z, k))^(2)- 1)= 1 - (k)^(2)*(1 - (JacobiND(z, k))^(2)) |
(k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1)= 1 - (k)^(2)*(1 - (JacobiND[z, (k)^2])^(2)) |
Failure | Failure | Fail 3.538045196-1.298501057*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-.1919889172e-1-.1946350456*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}.423148605e-1+.982010952*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}3.538045196+1.298501057*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[3.538045200949385, -1.2985010548545435] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.01919889241282169, -0.1946350457086099] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.04231486027619802, 0.9820109568681117] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.538045200949385, 1.2985010548545435] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{2z}{k} = \frac{2\Jacobiellsnk@{z}{k}\Jacobiellcnk@{z}{k}\Jacobielldnk@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | JacobiSN(2*z, k)=(2*JacobiSN(z, k)*JacobiCN(z, k)*JacobiDN(z, k))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
JacobiSN[2*z, (k)^2]=Divide[2*JacobiSN[z, (k)^2]*JacobiCN[z, (k)^2]*JacobiDN[z, (k)^2],1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Failure | Successful | Successful |
| 22.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{2z}{k} = \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | JacobiCN(2*z, k)=((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
JacobiCN[2*z, (k)^2]=Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Failure | Successful | Successful |
| 22.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobiellcnk^{4}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | ((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))=((JacobiCN(z, k))^(4)- 1 - (k)^(2)* (JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]=Divide[(JacobiCN[z, (k)^2])^(4)- 1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Failure | Fail -4.094154376+1.280458226*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-1.389457565+.616517316e-1*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}.8632946284-.6529631058*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-4.094154376-1.280458226*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-4.0941543674510195, 1.2804582127704043] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.3894575644075957, 0.06165173015688402] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8632946317597533, -0.6529631059321507] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.0941543674510195, -1.2804582127704043] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{2z}{k} = \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | JacobiDN(2*z, k)=((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
JacobiDN[2*z, (k)^2]=Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Failure | Successful | Successful |
| 22.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobielldnk^{4}@{z}{k}+k^{2}{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | ((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))=((JacobiDN(z, k))^(4)+ (k)^(2)* 1 - (k)^(2)* (JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]=Divide[(JacobiDN[z, (k)^2])^(4)+ (k)^(2)* 1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Failure | Fail -.9999999995-.2e-10*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}1.213361962-.134512870*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-8.242862557+3.616411048*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-.9999999995+.2e-10*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-0.9999999999999996, -8.326672684688674*^-17] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.213361958707478, -0.1345128657968393] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.24286257590017, 3.6164110482396037] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.9999999999999996, 8.326672684688674*^-17] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcdk@{2z}{k} = \frac{\Jacobiellcdk^{2}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellndk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}} | JacobiCD(2*z, k)=((JacobiCD(z, k))^(2)- 1 - (k)^(2)* (JacobiSD(z, k))^(2)* (JacobiND(z, k))^(2))/(1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD(z, k))^(4)) |
JacobiCD[2*z, (k)^2]=Divide[(JacobiCD[z, (k)^2])^(2)- 1 - (k)^(2)* (JacobiSD[z, (k)^2])^(2)* (JacobiND[z, (k)^2])^(2),1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD[z, (k)^2])^(4)] |
Failure | Failure | Fail .1370541185+.1873251287e-1*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}.5364817078-.4234624245*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-.1981753675-.1199254751*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}.1370541185-.1873251287e-1*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.13705411883745122, 0.018732512731960915] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5364817078278756, -0.42346242319671296] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.19817536922951154, -0.1199254747103525] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.13705411883745144, -0.018732512731960915] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsdk@{2z}{k} = \frac{2\Jacobiellsdk@{z}{k}\Jacobiellcdk@{z}{k}\Jacobiellndk@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}} | JacobiSD(2*z, k)=(2*JacobiSD(z, k)*JacobiCD(z, k)*JacobiND(z, k))/(1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD(z, k))^(4)) |
JacobiSD[2*z, (k)^2]=Divide[2*JacobiSD[z, (k)^2]*JacobiCD[z, (k)^2]*JacobiND[z, (k)^2],1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD[z, (k)^2])^(4)] |
Failure | Failure | Fail -8.411649228+2.496794499*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}.4171906607e-1-.5404871752*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}.4672486370e-1-.3344443629*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-8.411649228-2.496794499*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-8.411649235958867, 2.496794495227415] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.041719065906232006, -0.5404871748442961] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.046724863833304056, -0.33444436276903133] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.411649235958867, -2.496794495227415] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellndk@{2z}{k} = \frac{\Jacobiellndk^{2}@{z}{k}+k^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellcdk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}} | JacobiND(2*z, k)=((JacobiND(z, k))^(2)+ (k)^(2)* (JacobiSD(z, k))^(2)* (JacobiCD(z, k))^(2))/(1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD(z, k))^(4)) |
JacobiND[2*z, (k)^2]=Divide[(JacobiND[z, (k)^2])^(2)+ (k)^(2)* (JacobiSD[z, (k)^2])^(2)* (JacobiCD[z, (k)^2])^(2),1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD[z, (k)^2])^(4)] |
Failure | Failure | Fail -8.469613315+2.476300734*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-.2446575645+.5929818787*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-.5059779542e-1-.4472642739*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-8.469613315-2.476300734*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-8.469613322356564, 2.4763007298746587] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.24465756431597135, 0.5929818773302299] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.05059779615055053, -0.4472642742544212] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.469613322356564, -2.4763007298746587] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldck@{2z}{k} = \frac{\Jacobielldck^{2}@{z}{k}+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\Jacobiellnck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}} | JacobiDC(2*z, k)=((JacobiDC(z, k))^(2)+ 1 - (k)^(2)* (JacobiSC(z, k))^(2)* (JacobiNC(z, k))^(2))/(1 - 1 - (k)^(2)* (JacobiSC(z, k))^(4)) |
JacobiDC[2*z, (k)^2]=Divide[(JacobiDC[z, (k)^2])^(2)+ 1 - (k)^(2)* (JacobiSC[z, (k)^2])^(2)* (JacobiNC[z, (k)^2])^(2),1 - 1 - (k)^(2)* (JacobiSC[z, (k)^2])^(4)] |
Failure | Failure | Fail .2798628459+.1057645812*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}2.155279764+3.336838966*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-10.41618961+.723801634*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}.2798628459-.1057645812*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.27986284597445743, 0.1057645806458628] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.1552797720040004, 3.3368389687939786] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-10.416189608158701, 0.7238016559320513] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.27986284597445743, -0.1057645806458628] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnck@{2z}{k} = \frac{\Jacobiellnck^{2}@{z}{k}+\Jacobiellsck^{2}@{z}{k}\Jacobielldck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}} | JacobiNC(2*z, k)=((JacobiNC(z, k))^(2)+ (JacobiSC(z, k))^(2)* (JacobiDC(z, k))^(2))/(1 - 1 - (k)^(2)* (JacobiSC(z, k))^(4)) |
JacobiNC[2*z, (k)^2]=Divide[(JacobiNC[z, (k)^2])^(2)+ (JacobiSC[z, (k)^2])^(2)* (JacobiDC[z, (k)^2])^(2),1 - 1 - (k)^(2)* (JacobiSC[z, (k)^2])^(4)] |
Failure | Failure | Fail -8.445366052+2.504181595*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-2.348000820+.4644873082*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}.3919060714+4.559323678*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-8.445366052-2.504181595*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-8.4453660597032, 2.504181591384576] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.3480008192225705, 0.46448731013438893] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.39190608798513005, 4.559323684618953] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.4453660597032, -2.504181591384576] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsck@{2z}{k} = \frac{2\Jacobiellsck@{z}{k}\Jacobielldck@{z}{k}\Jacobiellnck@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}} | JacobiSC(2*z, k)=(2*JacobiSC(z, k)*JacobiDC(z, k)*JacobiNC(z, k))/(1 - 1 - (k)^(2)* (JacobiSC(z, k))^(4)) |
JacobiSC[2*z, (k)^2]=Divide[2*JacobiSC[z, (k)^2]*JacobiDC[z, (k)^2]*JacobiNC[z, (k)^2],1 - 1 - (k)^(2)* (JacobiSC[z, (k)^2])^(4)] |
Failure | Failure | Fail -8.387425493+2.524419001*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}1.765721394-.9866914128*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-.5663184000+3.386135413*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-8.387425493-2.524419001*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-8.387425500158386, 2.5244189972251565] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.7657213943311842, -0.9866914167974857] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5663183953417591, 3.3861354179416785] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.387425500158386, -2.5244189972251565] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnsk@{2z}{k} = \frac{\Jacobiellnsk^{4}@{z}{k}-k^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}} | JacobiNS(2*z, k)=((JacobiNS(z, k))^(4)- (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k)) |
JacobiNS[2*z, (k)^2]=Divide[(JacobiNS[z, (k)^2])^(4)- (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]] |
Failure | Failure | Successful | Successful |
| 22.6.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldsk@{2z}{k} = \frac{k^{2}{k^{\prime}}^{2}+\Jacobielldsk^{4}@{z}{k}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}} | JacobiDS(2*z, k)=((k)^(2)* 1 - (k)^(2)+ (JacobiDS(z, k))^(4))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k)) |
JacobiDS[2*z, (k)^2]=Divide[(k)^(2)* 1 - (k)^(2)+ (JacobiDS[z, (k)^2])^(4),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]] |
Failure | Failure | Fail -2.958056429-.877828454*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}1.088429910+2.208840486*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-2.958056429+.877828454*I <- {z = 2^(1/2)-I*2^(1/2), k = 2}1.088429910-2.208840486*I <- {z = 2^(1/2)-I*2^(1/2), k = 3}... skip entries to safe data |
Fail
Complex[-2.9580564228983786, -0.8778284568736507] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0884299045387233, 2.2088404891294435] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.958056422898387, 0.8778284568736494] <- {Rule[k, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.088429904538725, -2.2088404891294466] <- {Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcsk@{2z}{k} = \frac{\Jacobiellcsk^{4}@{z}{k}-{k^{\prime}}^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}} | JacobiCS(2*z, k)=((JacobiCS(z, k))^(4)- 1 - (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k)) |
JacobiCS[2*z, (k)^2]=Divide[(JacobiCS[z, (k)^2])^(4)- 1 - (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]] |
Failure | Failure | Fail -5.128303818+1.266734153*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}1.972037619+.5852189693*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-.2721074781-.5522101210*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-5.128303818-1.266734153*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-5.12830382438052, 1.2667341514547281] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.9720376152655872, 0.5852189712491013] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.2721074761346811, -0.5522101222823614] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.12830382438052, -1.2667341514547281] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1-\Jacobiellcnk@{2z}{k}}{1+\Jacobiellcnk@{2z}{k}} = \frac{\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{\Jacobiellcnk^{2}@{z}{k}}} | (1 - JacobiCN(2*z, k))/(1 + JacobiCN(2*z, k))=((JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/((JacobiCN(z, k))^(2)) |
Divide[1 - JacobiCN[2*z, (k)^2],1 + JacobiCN[2*z, (k)^2]]=Divide[(JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),(JacobiCN[z, (k)^2])^(2)] |
Failure | Failure | Successful | Successful |
| 22.6.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1-\Jacobielldnk@{2z}{k}}{1+\Jacobielldnk@{2z}{k}} = \frac{k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{\Jacobielldnk^{2}@{z}{k}}} | (1 - JacobiDN(2*z, k))/(1 + JacobiDN(2*z, k))=((k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/((JacobiDN(z, k))^(2)) |
Divide[1 - JacobiDN[2*z, (k)^2],1 + JacobiDN[2*z, (k)^2]]=Divide[(k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),(JacobiDN[z, (k)^2])^(2)] |
Failure | Failure | Successful | Successful |
| 22.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk^{2}@{\tfrac{1}{2}z}{k} = \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}}} | (JacobiSN((1)/(2)*z, k))^(2)=(1 - JacobiCN(z, k))/(1 + JacobiDN(z, k)) |
(JacobiSN[Divide[1,2]*z, (k)^2])^(2)=Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]] |
Failure | Failure | Successful | Successful |
| 22.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}} = \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}} | (1 - JacobiCN(z, k))/(1 + JacobiDN(z, k))=(1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) |
Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]]=Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] |
Successful | Successful | - | - |
| 22.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}-{k^{\prime}}^{2}}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}} | (1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))=(JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k)- 1 - (k)^(2))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k))) |
Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]=Divide[JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]- 1 - (k)^(2),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])] |
Failure | Failure | Skip | Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.45878538673953206, 0.3465757753125938] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.9906706508509473, -0.4762646080392824] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk^{2}@{\tfrac{1}{2}z}{k} = \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}} | (JacobiCN((1)/(2)*z, k))^(2)=(- 1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) |
(JacobiCN[Divide[1,2]*z, (k)^2])^(2)=Divide[- 1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] |
Failure | Failure | Fail 1.508209580+.7016668416*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-.5803980617-3.358394228*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}16.67395347+17.27038148*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}1.508209580-.7016668416*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[1.5082095810878147, 0.7016668414711776] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5803980702877369, -3.3583942301798655] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[16.673953528328266, 17.27038147971548] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.5082095810878147, -0.7016668414711776] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}} | (- 1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))=(1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k))) |
Divide[- 1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]=Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])] |
Failure | Failure | Fail Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}.4185282685+3.372883816*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-16.73162628-17.29201076*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.41852827726622005, 3.3728838175892157] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-16.731626338940483, -17.292010762136766] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1+\Jacobiellcnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}} | (1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k)))=(1 - (k)^(2)*(1 + JacobiCN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k)) |
Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])]=Divide[1 - (k)^(2)*(1 + JacobiCN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]] |
Failure | Failure | Skip | Fail
Complex[-0.07006090347484534, -0.11541357157973622] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.33824294612571393, 0.3972114524620808] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.07006090347484517, 0.11541357157973614] <- {Rule[k, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.33824294612571454, -0.3972114524620811] <- {Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk^{2}@{\tfrac{1}{2}z}{k} = \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}}} | (JacobiDN((1)/(2)*z, k))^(2)=((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+ 1 - (k)^(2))/(1 + JacobiDN(z, k)) |
(JacobiDN[Divide[1,2]*z, (k)^2])^(2)=Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+ 1 - (k)^(2),1 + JacobiDN[z, (k)^2]] |
Failure | Failure | Successful | Successful |
| 22.6.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}}} | ((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+ 1 - (k)^(2))/(1 + JacobiDN(z, k))=(1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k)) |
Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+ 1 - (k)^(2),1 + JacobiDN[z, (k)^2]]=Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]] |
Failure | Failure | Fail Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}.352520828+.579583496e-1*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}.480944700-.194663538*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.3525208279139327, 0.05795834963740132] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.4809447044900228, -0.19466354179159007] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1+\Jacobielldnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}} | (1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k))=(1 - (k)^(2)*(1 + JacobiDN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k)) |
Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]]=Divide[1 - (k)^(2)*(1 + JacobiDN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]] |
Failure | Failure | Skip | Fail
Complex[0.10198361655247856, 0.014552344162486408] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.10205512091915558, 0.18553829333350658] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.10198361655248034, -0.014552344162487074] <- {Rule[k, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.10205512091914493, -0.18553829333351368] <- {Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.6.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genJacobiellk{p}{q}^{2}@{\tfrac{1}{2}z}{k} = \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}} | genJacobiellk(p)*(q)^(2)* (1)/(2)*z*k =(genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k) |
genJacobiellk(p)*(q)^(2)* Divide[1,2]*z*k =Divide[genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k,genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k] |
Failure | Failure | Skip | Skip |
| 22.6.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}} = \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}}} | (genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k)=(genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k) |
Divide[genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k,genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k]=Divide[genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k,1 + genJacobiellk(r)*q* z*k] |
Failure | Failure | Skip | Skip |
| 22.6.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}} = \frac{\genJacobiellk{p}{r}@{z}{k}+1}{\genJacobiellk{q}{r}@{z}{k}+1}} | (genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k)=(genJacobiellk(p)*r* z*k + 1)/(genJacobiellk(q)*r* z*k + 1) |
Divide[genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k,1 + genJacobiellk(r)*q* z*k]=Divide[genJacobiellk(p)*r* z*k + 1,genJacobiellk(q)*r* z*k + 1] |
Failure | Failure | Skip | Skip |
| 22.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{k} = \frac{(1+k_{1})\Jacobiellsnk@{z/(1+k_{1})}{k_{1}}}{1+k_{1}\Jacobiellsnk^{2}@{z/(1+k_{1})}{k_{1}}}} | JacobiSN(z, k)=((1 + k[1])* JacobiSN(z/(1 + k[1]), k[1]))/(1 + k[1]*(JacobiSN(z/(1 + k[1]), k[1]))^(2)) |
JacobiSN[z, (k)^2]=Divide[(1 + Subscript[k, 1])* JacobiSN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2],1 + Subscript[k, 1]*(JacobiSN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2])^(2)] |
Failure | Failure | Fail .55864218e-1-.8664119331e-1*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 1}-.2250495657+.6319729879*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 2}-1.435242225+.239860557e-1*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 3}-.17665263e-1+.9799998387e-1*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Successful |
| 22.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{k} = \frac{\Jacobiellcnk@{z/(1+k_{1})}{k_{1}}\Jacobielldnk@{z/(1+k_{1})}{k_{1}}}{1+k_{1}\Jacobiellsnk^{2}@{z/(1+k_{1})}{k_{1}}}} | JacobiCN(z, k)=(JacobiCN(z/(1 + k[1]), k[1])*JacobiDN(z/(1 + k[1]), k[1]))/(1 + k[1]*(JacobiSN(z/(1 + k[1]), k[1]))^(2)) |
JacobiCN[z, (k)^2]=Divide[JacobiCN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2]*JacobiDN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2],1 + Subscript[k, 1]*(JacobiSN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2])^(2)] |
Failure | Failure | Fail -.2105289453-.565375351e-1*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 1}-1.400590390+1.028876610*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 2}-1.242789928+.3906876874*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 3}.2083630894+.417473069e-1*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Successful |
| 22.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{k} = \frac{\Jacobielldnk^{2}@{z/(1+k_{1})}{k_{1}}-(1-k_{1})}{1+k_{1}-\Jacobielldnk^{2}@{z/(1+k_{1})}{k_{1}}}} | JacobiDN(z, k)=((JacobiDN(z/(1 + k[1]), k[1]))^(2)-(1 - k[1]))/(1 + k[1]- (JacobiDN(z/(1 + k[1]), k[1]))^(2)) |
JacobiDN[z, (k)^2]=Divide[(JacobiDN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2])^(2)-(1 - Subscript[k, 1]),1 + Subscript[k, 1]- (JacobiDN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2])^(2)] |
Failure | Failure | Fail .1402363057-.923635469e-1*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 1}1.725656124-1.103604180*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 2}.7478105788+1.143211966*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)+I*2^(1/2), k = 3}-.1058691384+.765115293e-1*I <- {z = 2^(1/2)+I*2^(1/2), k[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Successful |
| 22.7.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{k} = \frac{(1+k^{\prime}_{2})\Jacobiellsnk@{z/(1+k^{\prime}_{2})}{k_{2}}\Jacobiellcnk@{z/(1+k^{\prime}_{2})}{k_{2}}}{\Jacobielldnk@{z/(1+k^{\prime}_{2})}{k_{2}}}} | JacobiSN(z, k)=((1 +sqrt(1 - (k)^(2))[2])* JacobiSN(z/(1 +sqrt(1 - (k)^(2))[2]), k[2])*JacobiCN(z/(1 +sqrt(1 - (k)^(2))[2]), k[2]))/(JacobiDN(z/(1 +sqrt(1 - (k)^(2))[2]), k[2])) |
JacobiSN[z, (k)^2]=Divide[(1 +Subscript[Sqrt[1 - (k)^(2)], 2])* JacobiSN[z/(1 +Subscript[Sqrt[1 - (k)^(2)], 2]), (Subscript[k, 2])^2]*JacobiCN[z/(1 +Subscript[Sqrt[1 - (k)^(2)], 2]), (Subscript[k, 2])^2],JacobiDN[z/(1 +Subscript[Sqrt[1 - (k)^(2)], 2]), (Subscript[k, 2])^2]] |
Failure | Failure | Error | Successful |
| 22.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{k} = \frac{(1+k^{\prime}_{2})(\Jacobielldnk^{2}@{z/(1+k^{\prime}_{2})}{k_{2}}-k^{\prime}_{2})}{k_{2}^{2}\Jacobielldnk@{z/(1+k^{\prime}_{2})}{k_{2}}}} | JacobiCN(z, k)((1 +sqrt(1 - (k)^(2))[2])*((JacobiDN(z/(1 +sqrt(1 - (k)^(2))[2]), k[2]))^(2)-sqrt(1 - (k)^(2))[2]))/(k(k[2])^(2)*JacobiDN(z/(1 +sqrt(1 - (k)^(2))[2]), k[2])) |
JacobiCN[z, (k)^2]Divide[(1 +Subscript[Sqrt[1 - (k)^(2)], 2])*((JacobiDN[z/(1 +Subscript[Sqrt[1 - (k)^(2)], 2]), (Subscript[k, 2])^2])^(2)-Subscript[Sqrt[1 - (k)^(2)], 2]),k(Subscript[k, 2])^(2)*JacobiDN[z/(1 +Subscript[Sqrt[1 - (k)^(2)], 2]), (Subscript[k, 2])^2]] |
Failure | Failure | Error | Successful |
| 22.7.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{k} = \frac{(1-k^{\prime}_{2})(\Jacobielldnk^{2}@{z/(1+k^{\prime}_{2})}{k_{2}}+k^{\prime}_{2})}{k_{2}^{2}\Jacobielldnk@{z/(1+k^{\prime}_{2})}{k_{2}}}} | JacobiDN(z, k)((1 -sqrt(1 - (k)^(2))[2])*((JacobiDN(z/(1 +sqrt(1 - (k)^(2))[2]), k[2]))^(2)+sqrt(1 - (k)^(2))[2]))/(k(k[2])^(2)*JacobiDN(z/(1 +sqrt(1 - (k)^(2))[2]), k[2])) |
JacobiDN[z, (k)^2]Divide[(1 -Subscript[Sqrt[1 - (k)^(2)], 2])*((JacobiDN[z/(1 +Subscript[Sqrt[1 - (k)^(2)], 2]), (Subscript[k, 2])^2])^(2)+Subscript[Sqrt[1 - (k)^(2)], 2]),k(Subscript[k, 2])^(2)*JacobiDN[z/(1 +Subscript[Sqrt[1 - (k)^(2)], 2]), (Subscript[k, 2])^2]] |
Failure | Failure | Error | Successful |
| 22.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}+\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}{1-k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}} | JacobiSN(u + v, k)=(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)+ JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k))/(1 - (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2)) |
JacobiSN[u + v, (k)^2]=Divide[JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]+ JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2],1 - (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2)] |
Successful | Failure | - | Skip |
| 22.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@@{(u+v)}{k} = \frac{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}-\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}{1-k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}} | JacobiCN(u + v, k)=(JacobiCN(u, k)*JacobiCN(v, k)- JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k))/(1 - (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2)) |
JacobiCN[u + v, (k)^2]=Divide[JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]- JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2],1 - (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2)] |
Successful | Failure | - | Successful |
| 22.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{(u+v)}{k} = \frac{\Jacobielldnk@@{u}{k}\Jacobielldnk@@{v}{k}-k^{2}\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{v}{k}}{1-k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}} | JacobiDN(u + v, k)=(JacobiDN(u, k)*JacobiDN(v, k)- (k)^(2)* JacobiSN(u, k)*JacobiCN(u, k)*JacobiSN(v, k)*JacobiCN(v, k))/(1 - (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2)) |
JacobiDN[u + v, (k)^2]=Divide[JacobiDN[u, (k)^2]*JacobiDN[v, (k)^2]- (k)^(2)* JacobiSN[u, (k)^2]*JacobiCN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiCN[v, (k)^2],1 - (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2)] |
Successful | Failure | - | Skip |
| 22.8.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcdk@@{(u+v)}{k} = \frac{\Jacobiellcdk@@{u}{k}\Jacobiellcdk@@{v}{k}-{k^{\prime}}^{2}\Jacobiellsdk@@{u}{k}\Jacobiellndk@@{u}{k}\Jacobiellsdk@@{v}{k}\Jacobiellndk@@{v}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@@{u}{k}\Jacobiellsdk^{2}@@{v}{k}}} | JacobiCD(u + v, k)=(JacobiCD(u, k)*JacobiCD(v, k)- 1 - (k)^(2)* JacobiSD(u, k)*JacobiND(u, k)*JacobiSD(v, k)*JacobiND(v, k))/(1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD(u, k))^(2)* (JacobiSD(v, k))^(2)) |
JacobiCD[u + v, (k)^2]=Divide[JacobiCD[u, (k)^2]*JacobiCD[v, (k)^2]- 1 - (k)^(2)* JacobiSD[u, (k)^2]*JacobiND[u, (k)^2]*JacobiSD[v, (k)^2]*JacobiND[v, (k)^2],1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD[u, (k)^2])^(2)* (JacobiSD[v, (k)^2])^(2)] |
Failure | Failure | Fail .1370541185+.1873251287e-1*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 1}.5364817078-.4234624245*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 2}-.1981753675-.1199254751*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 3}.1228104592+.1366601567e-11*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 22.8.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsdk@@{(u+v)}{k} = \frac{\Jacobiellsdk@@{u}{k}\Jacobiellcdk@@{v}{k}\Jacobiellndk@@{v}{k}+\Jacobiellsdk@@{v}{k}\Jacobiellcdk@@{u}{k}\Jacobiellndk@@{u}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@@{u}{k}\Jacobiellsdk^{2}@@{v}{k}}} | JacobiSD(u + v, k)=(JacobiSD(u, k)*JacobiCD(v, k)*JacobiND(v, k)+ JacobiSD(v, k)*JacobiCD(u, k)*JacobiND(u, k))/(1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD(u, k))^(2)* (JacobiSD(v, k))^(2)) |
JacobiSD[u + v, (k)^2]=Divide[JacobiSD[u, (k)^2]*JacobiCD[v, (k)^2]*JacobiND[v, (k)^2]+ JacobiSD[v, (k)^2]*JacobiCD[u, (k)^2]*JacobiND[u, (k)^2],1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD[u, (k)^2])^(2)* (JacobiSD[v, (k)^2])^(2)] |
Failure | Failure | Fail -8.411649228+2.496794499*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 1}.4171906607e-1-.5404871752*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 2}.4672486370e-1-.3344443629*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 3}8.845535938-0.*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 22.8.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellndk@@{(u+v)}{k} = \frac{\Jacobiellndk@@{u}{k}\Jacobiellndk@@{v}{k}+k^{2}\Jacobiellsdk@@{u}{k}\Jacobiellcdk@@{u}{k}\Jacobiellsdk@@{v}{k}\Jacobiellcdk@@{v}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@@{u}{k}\Jacobiellsdk^{2}@@{v}{k}}} | JacobiND(u + v, k)=(JacobiND(u, k)*JacobiND(v, k)+ (k)^(2)* JacobiSD(u, k)*JacobiCD(u, k)*JacobiSD(v, k)*JacobiCD(v, k))/(1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD(u, k))^(2)* (JacobiSD(v, k))^(2)) |
JacobiND[u + v, (k)^2]=Divide[JacobiND[u, (k)^2]*JacobiND[v, (k)^2]+ (k)^(2)* JacobiSD[u, (k)^2]*JacobiCD[u, (k)^2]*JacobiSD[v, (k)^2]*JacobiCD[v, (k)^2],1 + (k)^(2)* 1 - (k)^(2)* (JacobiSD[u, (k)^2])^(2)* (JacobiSD[v, (k)^2])^(2)] |
Failure | Failure | Fail -8.469613315+2.476300734*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 1}-.2446575645+.5929818787*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 2}-.5059779542e-1-.4472642739*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 3}8.907556175-0.*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-8.469613322356564, 2.4763007298746587] <- {Rule[k, 1], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.24465756431597135, 0.5929818773302299] <- {Rule[k, 2], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.05059779615055053, -0.4472642742544212] <- {Rule[k, 3], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.907556180814666, 0.0] <- {Rule[k, 1], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.8.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldck@@{(u+v)}{k} = \frac{\Jacobielldck@@{u}{k}\Jacobielldck@@{v}{k}+{k^{\prime}}^{2}\Jacobiellsck@@{u}{k}\Jacobiellnck@@{u}{k}\Jacobiellsck@@{v}{k}\Jacobiellnck@@{v}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{2}@@{u}{k}\Jacobiellsck^{2}@@{v}{k}}} | JacobiDC(u + v, k)=(JacobiDC(u, k)*JacobiDC(v, k)+ 1 - (k)^(2)* JacobiSC(u, k)*JacobiNC(u, k)*JacobiSC(v, k)*JacobiNC(v, k))/(1 - 1 - (k)^(2)* (JacobiSC(u, k))^(2)* (JacobiSC(v, k))^(2)) |
JacobiDC[u + v, (k)^2]=Divide[JacobiDC[u, (k)^2]*JacobiDC[v, (k)^2]+ 1 - (k)^(2)* JacobiSC[u, (k)^2]*JacobiNC[u, (k)^2]*JacobiSC[v, (k)^2]*JacobiNC[v, (k)^2],1 - 1 - (k)^(2)* (JacobiSC[u, (k)^2])^(2)* (JacobiSC[v, (k)^2])^(2)] |
Failure | Failure | Fail .2798628459+.1057645812*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 1}2.155279764+3.336838966*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 2}-10.41618961+.723801634*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 3}.2913197033+.1243926156e-11*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.27986284597445743, 0.1057645806458628] <- {Rule[k, 1], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.1552797720040004, 3.3368389687939786] <- {Rule[k, 2], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-10.416189608158701, 0.7238016559320513] <- {Rule[k, 3], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.2913197027505876, 0.0] <- {Rule[k, 1], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.8.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnck@@{(u+v)}{k} = \frac{\Jacobiellnck@@{u}{k}\Jacobiellnck@@{v}{k}+\Jacobiellsck@@{u}{k}\Jacobielldck@@{u}{k}\Jacobiellsck@@{v}{k}\Jacobielldck@@{v}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{2}@@{u}{k}\Jacobiellsck^{2}@@{v}{k}}} | JacobiNC(u + v, k)=(JacobiNC(u, k)*JacobiNC(v, k)+ JacobiSC(u, k)*JacobiDC(u, k)*JacobiSC(v, k)*JacobiDC(v, k))/(1 - 1 - (k)^(2)* (JacobiSC(u, k))^(2)* (JacobiSC(v, k))^(2)) |
JacobiNC[u + v, (k)^2]=Divide[JacobiNC[u, (k)^2]*JacobiNC[v, (k)^2]+ JacobiSC[u, (k)^2]*JacobiDC[u, (k)^2]*JacobiSC[v, (k)^2]*JacobiDC[v, (k)^2],1 - 1 - (k)^(2)* (JacobiSC[u, (k)^2])^(2)* (JacobiSC[v, (k)^2])^(2)] |
Failure | Failure | Fail -8.445366052+2.504181595*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 1}-2.348000820+.4644873082*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 2}.3919060714+4.559323678*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 3}8.869980794+0.*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-8.4453660597032, 2.504181591384576] <- {Rule[k, 1], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.3480008192225705, 0.46448731013438893] <- {Rule[k, 2], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.39190608798513005, 4.559323684618953] <- {Rule[k, 3], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.869980800731279, 0.0] <- {Rule[k, 1], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.8.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsck@@{(u+v)}{k} = \frac{\Jacobiellsck@@{u}{k}\Jacobielldck@@{v}{k}\Jacobiellnck@@{v}{k}+\Jacobiellsck@@{v}{k}\Jacobielldck@@{u}{k}\Jacobiellnck@@{u}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{2}@@{u}{k}\Jacobiellsck^{2}@@{v}{k}}} | JacobiSC(u + v, k)=(JacobiSC(u, k)*JacobiDC(v, k)*JacobiNC(v, k)+ JacobiSC(v, k)*JacobiDC(u, k)*JacobiNC(u, k))/(1 - 1 - (k)^(2)* (JacobiSC(u, k))^(2)* (JacobiSC(v, k))^(2)) |
JacobiSC[u + v, (k)^2]=Divide[JacobiSC[u, (k)^2]*JacobiDC[v, (k)^2]*JacobiNC[v, (k)^2]+ JacobiSC[v, (k)^2]*JacobiDC[u, (k)^2]*JacobiNC[u, (k)^2],1 - 1 - (k)^(2)* (JacobiSC[u, (k)^2])^(2)* (JacobiSC[v, (k)^2])^(2)] |
Failure | Failure | Fail -8.387425493+2.524419001*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 1}1.765721394-.9866914128*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 2}-.5663184000+3.386135413*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 3}8.808222182+0.*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-8.387425500158386, 2.5244189972251565] <- {Rule[k, 1], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.7657213943311842, -0.9866914167974857] <- {Rule[k, 2], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5663183953417591, 3.3861354179416785] <- {Rule[k, 3], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.808222188159213, 0.0] <- {Rule[k, 1], Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.8.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnsk@@{(u+v)}{k} = \frac{\Jacobiellnsk@@{u}{k}\Jacobielldsk@@{v}{k}\Jacobiellcsk@@{v}{k}-\Jacobiellnsk@@{v}{k}\Jacobielldsk@@{u}{k}\Jacobiellcsk@@{u}{k}}{\Jacobiellcsk^{2}@@{v}{k}-\Jacobiellcsk^{2}@@{u}{k}}} | JacobiNS(u + v, k)=(JacobiNS(u, k)*JacobiDS(v, k)*JacobiCS(v, k)- JacobiNS(v, k)*JacobiDS(u, k)*JacobiCS(u, k))/((JacobiCS(v, k))^(2)- (JacobiCS(u, k))^(2)) |
JacobiNS[u + v, (k)^2]=Divide[JacobiNS[u, (k)^2]*JacobiDS[v, (k)^2]*JacobiCS[v, (k)^2]- JacobiNS[v, (k)^2]*JacobiDS[u, (k)^2]*JacobiCS[u, (k)^2],(JacobiCS[v, (k)^2])^(2)- (JacobiCS[u, (k)^2])^(2)] |
Successful | Failure | - | Successful |
| 22.8.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldsk@@{(u+v)}{k} = \frac{\Jacobielldsk@@{u}{k}\Jacobiellcsk@@{v}{k}\Jacobiellnsk@@{v}{k}-\Jacobielldsk@@{v}{k}\Jacobiellcsk@@{u}{k}\Jacobiellnsk@@{u}{k}}{\Jacobiellcsk^{2}@@{v}{k}-\Jacobiellcsk^{2}@@{u}{k}}} | JacobiDS(u + v, k)=(JacobiDS(u, k)*JacobiCS(v, k)*JacobiNS(v, k)- JacobiDS(v, k)*JacobiCS(u, k)*JacobiNS(u, k))/((JacobiCS(v, k))^(2)- (JacobiCS(u, k))^(2)) |
JacobiDS[u + v, (k)^2]=Divide[JacobiDS[u, (k)^2]*JacobiCS[v, (k)^2]*JacobiNS[v, (k)^2]- JacobiDS[v, (k)^2]*JacobiCS[u, (k)^2]*JacobiNS[u, (k)^2],(JacobiCS[v, (k)^2])^(2)- (JacobiCS[u, (k)^2])^(2)] |
Successful | Failure | - | Successful |
| 22.8.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcsk@@{(u+v)}{k} = \frac{\Jacobiellcsk@@{u}{k}\Jacobielldsk@@{v}{k}\Jacobiellnsk@@{v}{k}-\Jacobiellcsk@@{v}{k}\Jacobielldsk@@{u}{k}\Jacobiellnsk@@{u}{k}}{\Jacobiellcsk^{2}@@{v}{k}-\Jacobiellcsk^{2}@@{u}{k}}} | JacobiCS(u + v, k)=(JacobiCS(u, k)*JacobiDS(v, k)*JacobiNS(v, k)- JacobiCS(v, k)*JacobiDS(u, k)*JacobiNS(u, k))/((JacobiCS(v, k))^(2)- (JacobiCS(u, k))^(2)) |
JacobiCS[u + v, (k)^2]=Divide[JacobiCS[u, (k)^2]*JacobiDS[v, (k)^2]*JacobiNS[v, (k)^2]- JacobiCS[v, (k)^2]*JacobiDS[u, (k)^2]*JacobiNS[u, (k)^2],(JacobiCS[v, (k)^2])^(2)- (JacobiCS[u, (k)^2])^(2)] |
Successful | Failure | - | Successful |
| 22.8.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@@{(u+v)}{k} = \frac{\Jacobiellsnk^{2}@@{u}{k}-\Jacobiellsnk^{2}@@{v}{k}}{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}} | JacobiSN(u + v, k)=((JacobiSN(u, k))^(2)- (JacobiSN(v, k))^(2))/(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k)) |
JacobiSN[u + v, (k)^2]=Divide[(JacobiSN[u, (k)^2])^(2)- (JacobiSN[v, (k)^2])^(2),JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]] |
Successful | Failure | - | Successful |
| 22.8.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{v}{k}+\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{u}{k}}{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}+\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}} | JacobiSN(u + v, k)=(JacobiSN(u, k)*JacobiCN(u, k)*JacobiDN(v, k)+ JacobiSN(v, k)*JacobiCN(v, k)*JacobiDN(u, k))/(JacobiCN(u, k)*JacobiCN(v, k)+ JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k)) |
JacobiSN[u + v, (k)^2]=Divide[JacobiSN[u, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[v, (k)^2]+ JacobiSN[v, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[u, (k)^2],JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]+ JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2]] |
Successful | Failure | - | Successful |
| 22.8.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{u}{k}}{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}} | JacobiCN(u + v, k)=(JacobiSN(u, k)*JacobiCN(u, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(v, k)*JacobiDN(u, k))/(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k)) |
JacobiCN[u + v, (k)^2]=Divide[JacobiSN[u, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[u, (k)^2],JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]] |
Successful | Failure | - | Successful |
| 22.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@@{(u+v)}{k} = \frac{1-\Jacobiellsnk^{2}@@{u}{k}-\Jacobiellsnk^{2}@@{v}{k}+k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}+\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}} | JacobiCN(u + v, k)=(1 - (JacobiSN(u, k))^(2)- (JacobiSN(v, k))^(2)+ (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2))/(JacobiCN(u, k)*JacobiCN(v, k)+ JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k)) |
JacobiCN[u + v, (k)^2]=Divide[1 - (JacobiSN[u, (k)^2])^(2)- (JacobiSN[v, (k)^2])^(2)+ (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2),JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]+ JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2]] |
Successful | Failure | - | Successful |
| 22.8.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{u}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{v}{k}}{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}} | JacobiDN(u + v, k)=(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(u, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(v, k))/(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k)) |
JacobiDN[u + v, (k)^2]=Divide[JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[u, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[v, (k)^2],JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]] |
Successful | Failure | - | Successful |
| 22.8.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{(u+v)}{k} = \frac{\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}+{k^{\prime}}^{2}\Jacobiellsnk@@{u}{k}\Jacobiellsnk@@{v}{k}}{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}+\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}} | JacobiDN(u + v, k)=(JacobiCN(u, k)*JacobiDN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)+ 1 - (k)^(2)* JacobiSN(u, k)*JacobiSN(v, k))/(JacobiCN(u, k)*JacobiCN(v, k)+ JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k)) |
JacobiDN[u + v, (k)^2]=Divide[JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]+ 1 - (k)^(2)* JacobiSN[u, (k)^2]*JacobiSN[v, (k)^2],JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]+ JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2]] |
Failure | Failure | Fail -.4438908315+.1804284132e-1*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 1}-.1432992406+.147150302*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 2}-.8677161564+.92219262e-1*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)+I*2^(1/2), k = 3}.4223716725-.4114809072e-11*I <- {u = 2^(1/2)+I*2^(1/2), v = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 22.8.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {k^{\prime}}^{2}-{k^{\prime}}^{2}k^{2}\Jacobiellsnk@@{z_{1}}{k}\Jacobiellsnk@@{z_{2}}{k}\Jacobiellsnk@@{z_{3}}{k}\Jacobiellsnk@@{z_{4}}{k}+k^{2}\Jacobiellcnk@@{z_{1}}{k}\Jacobiellcnk@@{z_{2}}{k}\Jacobiellcnk@@{z_{3}}{k}\Jacobiellcnk@@{z_{4}}{k}-\Jacobielldnk@@{z_{1}}{k}\Jacobielldnk@@{z_{2}}{k}\Jacobielldnk@@{z_{3}}{k}\Jacobielldnk@@{z_{4}}{k} = 0} | 1 - (k)^(2)- 1 - (k)^(2)* (k)^(2)* JacobiSN(z[1], k)*JacobiSN(z[2], k)*JacobiSN(z[3], k)*JacobiSN(z[4], k)+ (k)^(2)* JacobiCN(z[1], k)*JacobiCN(z[2], k)*JacobiCN(z[3], k)*JacobiCN(z[4], k)- JacobiDN(z[1], k)*JacobiDN(z[2], k)*JacobiDN(z[3], k)*JacobiDN(z[4], k)= 0 |
1 - (k)^(2)- 1 - (k)^(2)* (k)^(2)* JacobiSN[Subscript[z, 1], (k)^2]*JacobiSN[Subscript[z, 2], (k)^2]*JacobiSN[Subscript[z, 3], (k)^2]*JacobiSN[Subscript[z, 4], (k)^2]+ (k)^(2)* JacobiCN[Subscript[z, 1], (k)^2]*JacobiCN[Subscript[z, 2], (k)^2]*JacobiCN[Subscript[z, 3], (k)^2]*JacobiCN[Subscript[z, 4], (k)^2]- JacobiDN[Subscript[z, 1], (k)^2]*JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 3], (k)^2]*JacobiDN[Subscript[z, 4], (k)^2]= 0 |
Failure | Failure | Fail -2.551869041-.2283807357*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)+I*2^(1/2), k = 1}43.87494853-8.870468766*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)+I*2^(1/2), k = 2}-1.106498767+4.008029613*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)+I*2^(1/2), k = 3}-2.564399564-.1144957915*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 22.8.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}+z_{2}+z_{3}+z_{4} = 2\!\compellintKk@{k}} | z[1]+ z[2]+ z[3]+ z[4]= 2*EllipticK(k) |
Subscript[z, 1]+ Subscript[z, 2]+ Subscript[z, 3]+ Subscript[z, 4]= 2*EllipticK[(k)^2] |
Failure | Failure | Error | Skip |
| 22.8.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}-z_{2} = z_{2}-z_{3}} | z[1]- z[2]= z[2]- z[3] |
Subscript[z, 1]- Subscript[z, 2]= Subscript[z, 2]- Subscript[z, 3] |
Failure | Failure | Fail -2.828427124*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)-I*2^(1/2)}-2.828427124-2.828427124*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = -2^(1/2)-I*2^(1/2)}-2.828427124 <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = -2^(1/2)+I*2^(1/2)}5.656854248*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)-I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.0, -2.8284271247461903] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-2.8284271247461903 <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 5.656854249492381] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.8.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{2}-z_{3} = \tfrac{2}{3}\!\compellintKk@{k}} | z[2]- z[3]=(2)/(3)*EllipticK(k) |
Subscript[z, 2]- Subscript[z, 3]=Divide[2,3]*EllipticK[(k)^2] |
Failure | Failure | Error | Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.561916784937532, 0.7188385491665478] <- {Rule[k, 2], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.35941927458327383, 0.5619167849375319] <- {Rule[k, 3], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.8.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}-z_{2} = z_{2}-z_{3}} | z[1]- z[2]= z[2]- z[3] |
Subscript[z, 1]- Subscript[z, 2]= Subscript[z, 2]- Subscript[z, 3] |
Failure | Failure | Fail -2.828427124*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)-I*2^(1/2)}-2.828427124-2.828427124*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = -2^(1/2)-I*2^(1/2)}-2.828427124 <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = -2^(1/2)+I*2^(1/2)}5.656854248*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)-I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.0, -2.8284271247461903] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-2.8284271247461903 <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 5.656854249492381] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.8.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{2}-z_{3} = z_{3}-z_{4}} | z[2]- z[3]= z[3]- z[4] |
Subscript[z, 2]- Subscript[z, 3]= Subscript[z, 3]- Subscript[z, 4] |
Failure | Failure | Fail -2.828427124*I <- {z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)-I*2^(1/2)}-2.828427124-2.828427124*I <- {z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = -2^(1/2)-I*2^(1/2)}-2.828427124 <- {z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = -2^(1/2)+I*2^(1/2)}5.656854248*I <- {z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)-I*2^(1/2), z[4] = 2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.0, -2.8284271247461903] <- {Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-2.8284271247461903 <- {Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 5.656854249492381] <- {Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 3], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.8.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{3}-z_{4} = \tfrac{1}{2}\!\compellintKk@{k}} | z[3]- z[4]=(1)/(2)*EllipticK(k) |
Subscript[z, 3]- Subscript[z, 4]=Divide[1,2]*EllipticK[(k)^2] |
Failure | Failure | Skip | Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.42143758870314907, 0.5391289118749109] <- {Rule[k, 2], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.26956445593745537, 0.421437588703149] <- {Rule[k, 3], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[Subscript[z, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.8.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{z_{1}}{k}\Jacobielldnk@@{z_{3}}{k} = \Jacobielldnk@@{z_{2}}{k}\Jacobielldnk@@{z_{4}}{k}} | JacobiDN(z[1], k)*JacobiDN(z[3], k)= JacobiDN(z[2], k)*JacobiDN(z[4], k) |
JacobiDN[Subscript[z, 1], (k)^2]*JacobiDN[Subscript[z, 3], (k)^2]= JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 4], (k)^2] |
Failure | Failure | Fail -.5144265506-.9141882921e-1*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)-I*2^(1/2), k = 1}-4.611092996-5.088311894*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)-I*2^(1/2), k = 2}-1.061172547+1.016431323*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)-I*2^(1/2), k = 3}-.5144265506-.9141882921e-1*I <- {z[1] = 2^(1/2)+I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2), z[3] = 2^(1/2)+I*2^(1/2), z[4] = -2^(1/2)+I*2^(1/2), k = 1}... skip entries to safe data |
Skip |
| 22.8.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{z_{2}}{k}\Jacobielldnk@@{z_{4}}{k} = k^{\prime}} | JacobiDN(z[2], k)*JacobiDN(z[4], k)=sqrt(1 - (k)^(2)) |
JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 4], (k)^2]=Sqrt[1 - (k)^(2)] |
Failure | Failure | Fail -.2490902475-.9141882921e-1*I <- {z[2] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)+I*2^(1/2), k = 1}.5019134627-6.820362702*I <- {z[2] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)+I*2^(1/2), k = 2}-.4379803287e-1-1.811995802*I <- {z[2] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)+I*2^(1/2), k = 3}.2653363031+0.*I <- {z[2] = 2^(1/2)+I*2^(1/2), z[4] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-0.2490902473433826, -0.0914188289178922] <- {Rule[k, 1], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5019134769388622, -6.820362696879865] <- {Rule[k, 2], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.04379803397253301, -1.8119958055932632] <- {Rule[k, 3], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.26533630283530063, 0.0] <- {Rule[k, 1], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 4], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{m,p}^{(2)} = \Jacobiellsnk@{z+2p^{-1}(m-1)\compellintKk@{k}}{k}} | (s[m , p])^(2)= JacobiSN(z + 2*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[s, m , p])^(2)= JacobiSN[z + 2*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Skip |
| 22.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{m,p}^{(2)} = \Jacobiellcnk@{z+2p^{-1}(m-1)\compellintKk@{k}}{k}} | (c[m , p])^(2)= JacobiCN(z + 2*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[c, m , p])^(2)= JacobiCN[z + 2*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Skip |
| 22.9.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{m,p}^{(2)} = \Jacobielldnk@{z+2p^{-1}(m-1)\compellintKk@{k}}{k}} | (d[m , p])^(2)= JacobiDN(z + 2*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[d, m , p])^(2)= JacobiDN[z + 2*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Skip |
| 22.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{m,p}^{(4)} = \Jacobiellsnk@{z+4p^{-1}(m-1)\compellintKk@{k}}{k}} | (s[m , p])^(4)= JacobiSN(z + 4*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[s, m , p])^(4)= JacobiSN[z + 4*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Skip |
| 22.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{m,p}^{(4)} = \Jacobiellcnk@{z+4p^{-1}(m-1)\compellintKk@{k}}{k}} | (c[m , p])^(4)= JacobiCN(z + 4*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[c, m , p])^(4)= JacobiCN[z + 4*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Skip |
| 22.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{m,p}^{(4)} = \Jacobielldnk@{z+4p^{-1}(m-1)\compellintKk@{k}}{k}} | (d[m , p])^(4)= JacobiDN(z + 4*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[d, m , p])^(4)= JacobiDN[z + 4*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Skip |
| 22.9.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \kappa = \Jacobielldnk@{2\!\compellintKk@{k}/3}{k}} | kappa = JacobiDN(2*EllipticK(k)/ 3, k) |
\[Kappa]= JacobiDN[2*EllipticK[(k)^2]/ 3, (k)^2] |
Failure | Failure | Error | Fail
Complex[0.8378491740658316, -0.012111700392196889] <- {Rule[k, 2], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5354591881471004, -0.6433228556445936] <- {Rule[k, 3], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8378491740658316, -2.8405388251383874] <- {Rule[k, 2], Rule[κ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.5354591881471004, -3.4717499803907836] <- {Rule[k, 3], Rule[κ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.11.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}} | JacobiSN(z, k)=(2*Pi)/(K*k)*sum(((q)^(n +(1)/(2))* sin((2*n + 1)* zeta))/(1 - (q)^(2*n + 1)), n = 0..infinity) |
JacobiSN[z, (k)^2]=Divide[2*Pi,K*k]*Sum[Divide[(q)^(n +Divide[1,2])* Sin[(2*n + 1)* \[zeta]],1 - (q)^(2*n + 1)], {n, 0, Infinity}] |
Error | Failure | - | Error |
| 22.11.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}} | JacobiCN(z, k)=(2*Pi)/(K*k)*sum(((q)^(n +(1)/(2))* cos((2*n + 1)* zeta))/(1 + (q)^(2*n + 1)), n = 0..infinity) |
JacobiCN[z, (k)^2]=Divide[2*Pi,K*k]*Sum[Divide[(q)^(n +Divide[1,2])* Cos[(2*n + 1)* \[zeta]],1 + (q)^(2*n + 1)], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{k} = \frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}\cos@{2n\zeta}}{1+q^{2n}}} | JacobiDN(z, k)=(Pi)/(2*EllipticK(k))+(2*Pi)/(EllipticK(k))*sum(((q)^(n)* cos(2*n*zeta))/(1 + (q)^(2*n)), n = 1..infinity) |
JacobiDN[z, (k)^2]=Divide[Pi,2*EllipticK[(k)^2]]+Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(q)^(n)* Cos[2*n*\[zeta]],1 + (q)^(2*n)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcdk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}} | JacobiCD(z, k)=(2*Pi)/(K*k)*sum(((- 1)^(n)* (q)^(n +(1)/(2))* cos((2*n + 1)* zeta))/(1 - (q)^(2*n + 1)), n = 0..infinity) |
JacobiCD[z, (k)^2]=Divide[2*Pi,K*k]*Sum[Divide[(- 1)^(n)* (q)^(n +Divide[1,2])* Cos[(2*n + 1)* \[zeta]],1 - (q)^(2*n + 1)], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsdk@{z}{k} = \frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}} | JacobiSD(z, k)=(2*Pi)/(K*k*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)* (q)^(n +(1)/(2))* sin((2*n + 1)* zeta))/(1 + (q)^(2*n + 1)), n = 0..infinity) |
JacobiSD[z, (k)^2]=Divide[2*Pi,K*k*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)* (q)^(n +Divide[1,2])* Sin[(2*n + 1)* \[zeta]],1 + (q)^(2*n + 1)], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellndk@{z}{k} = \frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos@{2n\zeta}}{1+q^{2n}}} | JacobiND(z, k)=(Pi)/(2*K*sqrt(1 - (k)^(2)))+(2*Pi)/(K*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)* (q)^(n)* cos(2*n*zeta))/(1 + (q)^(2*n)), n = 1..infinity) |
JacobiND[z, (k)^2]=Divide[Pi,2*K*Sqrt[1 - (k)^(2)]]+Divide[2*Pi,K*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)* (q)^(n)* Cos[2*n*\[zeta]],1 + (q)^(2*n)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}} | JacobiNS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta)=(2*Pi)/(EllipticK(k))*sum(((q)^(2*n + 1)* sin((2*n + 1)* zeta))/(1 - (q)^(2*n + 1)), n = 0..infinity) |
JacobiNS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[zeta]]=Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(q)^(2*n + 1)* Sin[(2*n + 1)* \[zeta]],1 - (q)^(2*n + 1)], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = -\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}} | JacobiDS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta)= -(2*Pi)/(EllipticK(k))*sum(((q)^(2*n + 1)* sin((2*n + 1)* zeta))/(1 + (q)^(2*n + 1)), n = 0..infinity) |
JacobiDS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[zeta]]= -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(q)^(2*n + 1)* Sin[(2*n + 1)* \[zeta]],1 + (q)^(2*n + 1)], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcsk@{z}{k}-\frac{\pi}{2K}\cot@@{\zeta} = -\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\sin@{2n\zeta}}{1+q^{2n}}} | JacobiCS(z, k)-(Pi)/(2*EllipticK(k))*cot(zeta)= -(2*Pi)/(EllipticK(k))*sum(((q)^(2*n)* sin(2*n*zeta))/(1 + (q)^(2*n)), n = 1..infinity) |
JacobiCS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Cot[\[zeta]]= -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(q)^(2*n)* Sin[2*n*\[zeta]],1 + (q)^(2*n)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}} | JacobiDC(z, k)-(Pi)/(2*EllipticK(k))*sec(zeta)=(2*Pi)/(EllipticK(k))*sum(((- 1)^(n)* (q)^(2*n + 1)* cos((2*n + 1)* zeta))/(1 - (q)^(2*n + 1)), n = 0..infinity) |
JacobiDC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Sec[\[zeta]]=Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(- 1)^(n)* (q)^(2*n + 1)* Cos[(2*n + 1)* \[zeta]],1 - (q)^(2*n + 1)], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\sec@@{\zeta} = -\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}} | JacobiNC(z, k)-(Pi)/(2*K*sqrt(1 - (k)^(2)))*sec(zeta)= -(2*Pi)/(K*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)* (q)^(2*n + 1)* cos((2*n + 1)* zeta))/(1 + (q)^(2*n + 1)), n = 0..infinity) |
JacobiNC[z, (k)^2]-Divide[Pi,2*K*Sqrt[1 - (k)^(2)]]*Sec[\[zeta]]= -Divide[2*Pi,K*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)* (q)^(2*n + 1)* Cos[(2*n + 1)* \[zeta]],1 + (q)^(2*n + 1)], {n, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\tan@@{\zeta} = \frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin@{2n\zeta}}{1+q^{2n}}} | JacobiSC(z, k)-(Pi)/(2*K*sqrt(1 - (k)^(2)))*tan(zeta)=(2*Pi)/(K*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)* (q)^(2*n)* sin(2*n*zeta))/(1 + (q)^(2*n)), n = 1..infinity) |
JacobiSC[z, (k)^2]-Divide[Pi,2*K*Sqrt[1 - (k)^(2)]]*Tan[\[zeta]]=Divide[2*Pi,K*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)* (q)^(2*n)* Sin[2*n*\[zeta]],1 + (q)^(2*n)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk^{2}@{z}{k} = \frac{1}{k^{2}}\left(1-\frac{\compellintEk@@{k}}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}\cos@{2n\zeta}} | (JacobiSN(z, k))^(2)=(1)/((k)^(2))*(1 -(EllipticE(k))/(EllipticK(k)))-(2*(Pi)^(2))/((k)^(2)* (EllipticK(k))^(2))*sum((n*(q)^(n))/(1 - (q)^(2*n))*cos(2*n*zeta), n = 1..infinity) |
(JacobiSN[z, (k)^2])^(2)=Divide[1,(k)^(2)]*(1 -Divide[EllipticE[(k)^2],EllipticK[(k)^2]])-Divide[2*(Pi)^(2),(k)^(2)* (EllipticK[(k)^2])^(2)]*Sum[Divide[n*(q)^(n),1 - (q)^(2*n)]*Cos[2*n*\[zeta]], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 22.11.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}\Jacobiellsnk^{2}@{z}{k} = \frac{\ccompellintEk@@{k}}{\ccompellintKk@@{k}}-\left(\frac{\pi}{2\!\ccompellintKk}\right)^{2}\sum_{n=-\infty}^{\infty}\left(\sech^{2}@{\frac{\pi}{2\!\ccompellintKk@@{k}}(z-2n\!\compellintKk@@{k})}\right)} | (k)^(2)* (JacobiSN(z, k))^(2)=(EllipticCE(k))/(EllipticCK(k))-((Pi)/(2*EllipticCK($0)))^(2)* sum((sech((Pi)/(2*EllipticCK(k))*(z - 2*n*EllipticK(k))))^(2), n = - infinity..infinity) |
(k)^(2)* (JacobiSN[z, (k)^2])^(2)=Divide[EllipticE[1-(k)^2],EllipticK[1-(k)^2]]-(Divide[Pi,2*EllipticK[1-($0)^2]])^(2)* Sum[(Sech[Divide[Pi,2*EllipticK[1-(k)^2]]*(z - 2*n*EllipticK[(k)^2])])^(2), {n, - Infinity, Infinity}] |
Error | Failure | - | Error |
| 22.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau = i\ccompellintKk@{k}/\compellintKk@{k}} | tau = I*EllipticCK(k)/ EllipticK(k) |
\[Tau]= I*EllipticK[1-(k)^2]/ EllipticK[(k)^2] |
Failure | Failure | Error | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[k, 1], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.034924298733449, 0.929003383041147] <- {Rule[k, 2], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.1238725324006347, 0.9602938378765811] <- {Rule[k, 3], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[k, 1], Rule[τ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.12.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2Kk\Jacobiellsnk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}}} | 2*K*k*JacobiSN(2*K*t, k)= sum((Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity) |
2*K*k*JacobiSN[2*K*t, (k)^2]= Sum[Divide[Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 22.12.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t-m-(n+\frac{1}{2})\tau}\right)} | sum((Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity)= sum(sum(((- 1)^(m))/(t - m -(n +(1)/(2))* tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}]= Sum[Sum[Divide[(- 1)^(m),t - m -(n +Divide[1,2])* \[Tau]], {m, - Infinity, Infinity}], {n, - Infinity, Infinity}] |
Error | Failure | - | Error |
| 22.12.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2iKk\Jacobiellcnk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}}} | 2*I*K*k*JacobiCN(2*K*t, k)= sum(((- 1)^(n)* Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity) |
2*I*K*k*JacobiCN[2*K*t, (k)^2]= Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}] |
Failure | Failure | Skip | Skip |
| 22.12.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t-m-(n+\frac{1}{2})\tau}\right)} | sum(((- 1)^(n)* Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity)= sum(sum(((- 1)^(m + n))/(t - m -(n +(1)/(2))* tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}]= Sum[Sum[Divide[(- 1)^(m + n),t - m -(n +Divide[1,2])* \[Tau]], {m, - Infinity, Infinity}], {n, - Infinity, Infinity}] |
Error | Failure | - | Error |
| 22.12.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2K\Jacobielldck@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}}} | 2*EllipticK(k)*JacobiDC(2*K*t, k)= sum((Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity) |
2*EllipticK[(k)^2]*JacobiDC[2*K*t, (k)^2]= Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 22.12.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t+\frac{1}{2}-m-n\tau}\right)} | sum((Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity)= sum(sum(((- 1)^(m))/(t +(1)/(2)- m - n*tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}]= Sum[Sum[Divide[(- 1)^(m),t +Divide[1,2]- m - n*\[Tau]], {m, - Infinity, Infinity}], {n, - Infinity, Infinity}] |
Error | Failure | - | Error |
| 22.12.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2Kk^{\prime}\Jacobiellnck@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}}} | 2*K*sqrt(1 - (k)^(2))*JacobiNC(2*K*t, k)= sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity) |
2*K*Sqrt[1 - (k)^(2)]*JacobiNC[2*K*t, (k)^2]= Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}] |
Failure | Failure | Skip | Skip |
| 22.12.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t+\frac{1}{2}-m-n\tau}\right)} | sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity)= sum(sum(((- 1)^(m + n))/(t +(1)/(2)- m - n*tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}]= Sum[Sum[Divide[(- 1)^(m + n),t +Divide[1,2]- m - n*\[Tau]], {m, - Infinity, Infinity}], {n, - Infinity, Infinity}] |
Error | Failure | - | Error |
| 22.12.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2K\Jacobiellnsk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-n\tau)}}} | 2*EllipticK(k)*JacobiNS(2*K*t, k)= sum((Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity) |
2*EllipticK[(k)^2]*JacobiNS[2*K*t, (k)^2]= Sum[Divide[Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}] |
Failure | Failure | Skip | Skip |
| 22.12.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t-m-n\tau}\right)} | sum((Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity)= sum(sum(((- 1)^(m))/(t - m - n*tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}]= Sum[Sum[Divide[(- 1)^(m),t - m - n*\[Tau]], {m, - Infinity, Infinity}], {n, - Infinity, Infinity}] |
Error | Failure | - | Error |
| 22.12.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2K\Jacobielldsk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-n\tau)}}} | 2*EllipticK(k)*JacobiDS(2*K*t, k)= sum(((- 1)^(n)* Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity) |
2*EllipticK[(k)^2]*JacobiDS[2*K*t, (k)^2]= Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}] |
Failure | Failure | Skip | Skip |
| 22.12.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t-m-n\tau}\right)} | sum(((- 1)^(n)* Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity)= sum(sum(((- 1)^(m + n))/(t - m - n*tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}]= Sum[Sum[Divide[(- 1)^(m + n),t - m - n*\[Tau]], {m, - Infinity, Infinity}], {n, - Infinity, Infinity}] |
Error | Failure | - | Error |
| 22.13.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellsnk@{z}{k}\right)^{2} = \left(1-\Jacobiellsnk^{2}@{z}{k}\right)\left(1-k^{2}\Jacobiellsnk^{2}@{z}{k}\right)} | (diff(JacobiSN(z, k), z))^(2)=(1 - (JacobiSN(z, k))^(2))*(1 - (k)^(2)* (JacobiSN(z, k))^(2)) |
(D[JacobiSN[z, (k)^2], z])^(2)=(1 - (JacobiSN[z, (k)^2])^(2))*(1 - (k)^(2)* (JacobiSN[z, (k)^2])^(2)) |
Successful | Successful | - | - |
| 22.13.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellcnk@{z}{k}\right)^{2} = {\left(1-\Jacobiellcnk^{2}@{z}{k}\right)}{\left({k^{\prime}}^{2}+k^{2}\Jacobiellcnk^{2}@{z}{k}\right)}} | (diff(JacobiCN(z, k), z))^(2)=(1 - (JacobiCN(z, k))^(2))*(1 - (k)^(2)+ (k)^(2)* (JacobiCN(z, k))^(2)) |
(D[JacobiCN[z, (k)^2], z])^(2)=(1 - (JacobiCN[z, (k)^2])^(2))*(1 - (k)^(2)+ (k)^(2)* (JacobiCN[z, (k)^2])^(2)) |
Successful | Successful | - | - |
| 22.13.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobielldnk@{z}{k}\right)^{2} = \left(1-\Jacobielldnk^{2}@{z}{k}\right)\left(\Jacobielldnk^{2}@{z}{k}-{k^{\prime}}^{2}\right)} | (diff(JacobiDN(z, k), z))^(2)=(1 - (JacobiDN(z, k))^(2))*((JacobiDN(z, k))^(2)- 1 - (k)^(2)) |
(D[JacobiDN[z, (k)^2], z])^(2)=(1 - (JacobiDN[z, (k)^2])^(2))*((JacobiDN[z, (k)^2])^(2)- 1 - (k)^(2)) |
Failure | Failure | Fail 2.498180497+.1828376586*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}3.98469228+40.70649515*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}18.78836459-18.29576381*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}2.498180497-.1828376586*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[2.4981804946867654, 0.18283765783578443] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.9846921844891163, 40.70649511448791] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[18.78836461150559, -18.29576374475269] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.4981804946867654, -0.18283765783578443] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellcdk@{z}{k}\right)^{2} = \left(1-\Jacobiellcdk^{2}@{z}{k}\right)\left(1-k^{2}\Jacobiellcdk^{2}@{z}{k}\right)} | (diff(JacobiCD(z, k), z))^(2)=(1 - (JacobiCD(z, k))^(2))*(1 - (k)^(2)* (JacobiCD(z, k))^(2)) |
(D[JacobiCD[z, (k)^2], z])^(2)=(1 - (JacobiCD[z, (k)^2])^(2))*(1 - (k)^(2)* (JacobiCD[z, (k)^2])^(2)) |
Successful | Successful | - | - |
| 22.13.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellsdk@{z}{k}\right)^{2} = {\left(1-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\right)}{\left(1+k^{2}\Jacobiellsdk^{2}@{z}{k}\right)}} | (diff(JacobiSD(z, k), z))^(2)=(1 - 1 - (k)^(2)* (JacobiSD(z, k))^(2))*(1 + (k)^(2)* (JacobiSD(z, k))^(2)) |
(D[JacobiSD[z, (k)^2], z])^(2)=(1 - 1 - (k)^(2)* (JacobiSD[z, (k)^2])^(2))*(1 + (k)^(2)* (JacobiSD[z, (k)^2])^(2)) |
Failure | Failure | Fail 10.83165880-9.188310853*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-.8004902522e-1-.1328975640*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-1.780546172+1.029879100*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}10.83165880+9.188310853*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[10.831658854502608, -9.188310851111659] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.08004902551881446, -0.13289756372332284] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7805461824378226, 1.0298791081722538] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[10.831658854502608, 9.188310851111659] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellndk@{z}{k}\right)^{2} = \left(\Jacobiellndk^{2}@{z}{k}-1\right)\left(1-{k^{\prime}}^{2}\Jacobiellndk^{2}@{z}{k}\right)} | (diff(JacobiND(z, k), z))^(2)=((JacobiND(z, k))^(2)- 1)*(1 - 1 - (k)^(2)* (JacobiND(z, k))^(2)) |
(D[JacobiND[z, (k)^2], z])^(2)=((JacobiND[z, (k)^2])^(2)- 1)*(1 - 1 - (k)^(2)* (JacobiND[z, (k)^2])^(2)) |
Failure | Failure | Fail 9.831658819-9.188310855*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-1.377792776-1.115495393*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-16.68639667+17.12499953*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}9.831658819+9.188310855*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[9.831658854502614, -9.188310851111664] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.3777927793137241, -1.115495392019118] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-16.686396759730812, 17.124999628495146] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.831658854502614, 9.188310851111664] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobielldck@{z}{k}\right)^{2} = \left(\Jacobielldck^{2}@{z}{k}-1\right)\left(\Jacobielldck^{2}@{z}{k}-k^{2}\right)} | (diff(JacobiDC(z, k), z))^(2)=((JacobiDC(z, k))^(2)- 1)*((JacobiDC(z, k))^(2)- (k)^(2)) |
(D[JacobiDC[z, (k)^2], z])^(2)=((JacobiDC[z, (k)^2])^(2)- 1)*((JacobiDC[z, (k)^2])^(2)- (k)^(2)) |
Successful | Successful | - | - |
| 22.13.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellnck@{z}{k}\right)^{2} = {\left(k^{2}+{k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}\right)}{\left(\Jacobiellnck^{2}@{z}{k}-1\right)}} | (diff(JacobiNC(z, k), z))^(2)=((k)^(2)+ 1 - (k)^(2)* (JacobiNC(z, k))^(2))*((JacobiNC(z, k))^(2)- 1) |
(D[JacobiNC[z, (k)^2], z])^(2)=((k)^(2)+ 1 - (k)^(2)* (JacobiNC[z, (k)^2])^(2))*((JacobiNC[z, (k)^2])^(2)- 1) |
Failure | Failure | Fail 18.90774921-11.78531296*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}.1159583621-.675201614*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-.74436492e-2-.321433941e-1*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}18.90774921+11.78531296*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[18.907749256401388, -11.78531296082075] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.11595836325807751, -0.6752016132739329] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.007443648638819578, -0.032143394714381934] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[18.907749256401388, 11.78531296082075] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellsck@{z}{k}\right)^{2} = \left(1+\Jacobiellsck^{2}@{z}{k}\right)\left(1+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\right)} | (diff(JacobiSC(z, k), z))^(2)=(1 + (JacobiSC(z, k))^(2))*(1 + 1 - (k)^(2)* (JacobiSC(z, k))^(2)) |
(D[JacobiSC[z, (k)^2], z])^(2)=(1 + (JacobiSC[z, (k)^2])^(2))*(1 + 1 - (k)^(2)* (JacobiSC[z, (k)^2])^(2)) |
Failure | Failure | Fail 17.90774919-11.78531296*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-.884041635-.6752016142*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-1.007443648-.32143393e-1*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}17.90774919+11.78531296*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[17.90774925640138, -11.785312960820747] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8840416367419195, -0.6752016132739348] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0074436486388192, -0.032143394714381435] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[17.90774925640138, 11.785312960820747] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellnsk@{z}{k}\right)^{2} = \left(\Jacobiellnsk^{2}@{z}{k}-k^{2}\right)\left(\Jacobiellnsk^{2}@{z}{k}-1\right)} | (diff(JacobiNS(z, k), z))^(2)=((JacobiNS(z, k))^(2)- (k)^(2))*((JacobiNS(z, k))^(2)- 1) |
(D[JacobiNS[z, (k)^2], z])^(2)=((JacobiNS[z, (k)^2])^(2)- (k)^(2))*((JacobiNS[z, (k)^2])^(2)- 1) |
Successful | Successful | - | - |
| 22.13.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobielldsk@{z}{k}\right)^{2} = \left(\Jacobielldsk^{2}@{z}{k}-{k^{\prime}}^{2}\right)\left(k^{2}+\Jacobielldsk^{2}@{z}{k}\right)} | (diff(JacobiDS(z, k), z))^(2)=((JacobiDS(z, k))^(2)- 1 - (k)^(2))*((k)^(2)+ (JacobiDS(z, k))^(2)) |
(D[JacobiDS[z, (k)^2], z])^(2)=((JacobiDS[z, (k)^2])^(2)- 1 - (k)^(2))*((k)^(2)+ (JacobiDS[z, (k)^2])^(2)) |
Failure | Failure | Fail 1.592634334-.1165622473*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}.6097694629-6.229233331*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}79.66246105+77.57383910*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}1.592634334+.1165622473*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[1.5926343353666734, -0.11656224691795349] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.6097694563192116, -6.229233337330877] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[79.66246130818148, 77.57383899860325] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.5926343353666734, 0.11656224691795349] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellcsk@{z}{k}\right)^{2} = \left(1+\Jacobiellcsk^{2}@{z}{k}\right)\left({k^{\prime}}^{2}+\Jacobiellcsk^{2}@{z}{k}\right)} | (diff(JacobiCS(z, k), z))^(2)=(1 + (JacobiCS(z, k))^(2))*(1 - (k)^(2)+ (JacobiCS(z, k))^(2)) |
(D[JacobiCS[z, (k)^2], z])^(2)=(1 + (JacobiCS[z, (k)^2])^(2))*(1 - (k)^(2)+ (JacobiCS[z, (k)^2])^(2)) |
Successful | Successful | - | - |
| 22.13.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellsnk@{z}{k} = -(1+k^{2})\Jacobiellsnk@{z}{k}+2k^{2}\Jacobiellsnk^{3}@{z}{k}} | diff(JacobiSN(z, k), [z$(2)])= -(1 + (k)^(2))* JacobiSN(z, k)+ 2*(k)^(2)* (JacobiSN(z, k))^(3) |
D[JacobiSN[z, (k)^2], {z, 2}]= -(1 + (k)^(2))* JacobiSN[z, (k)^2]+ 2*(k)^(2)* (JacobiSN[z, (k)^2])^(3) |
Successful | Successful | - | - |
| 22.13.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellcnk@{z}{k} = -({k^{\prime}}^{2}-k^{2})\Jacobiellcnk@{z}{k}-2k^{2}\Jacobiellcnk^{3}@{z}{k}} | diff(JacobiCN(z, k), [z$(2)])= -(1 - (k)^(2)- (k)^(2))* JacobiCN(z, k)- 2*(k)^(2)* (JacobiCN(z, k))^(3) |
D[JacobiCN[z, (k)^2], {z, 2}]= -(1 - (k)^(2)- (k)^(2))* JacobiCN[z, (k)^2]- 2*(k)^(2)* (JacobiCN[z, (k)^2])^(3) |
Successful | Successful | - | - |
| 22.13.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobielldnk@{z}{k} = (1+{k^{\prime}}^{2})\Jacobielldnk@{z}{k}-2\Jacobielldnk^{3}@{z}{k}} | diff(JacobiDN(z, k), [z$(2)])=(1 + 1 - (k)^(2))* JacobiDN(z, k)- 2*(JacobiDN(z, k))^(3) |
D[JacobiDN[z, (k)^2], {z, 2}]=(1 + 1 - (k)^(2))* JacobiDN[z, (k)^2]- 2*(JacobiDN[z, (k)^2])^(3) |
Successful | Successful | - | - |
| 22.13.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellcdk@{z}{k} = -(1+k^{2})\Jacobiellcdk@{z}{k}+2k^{2}\Jacobiellcdk^{3}@{z}{k}} | diff(JacobiCD(z, k), [z$(2)])= -(1 + (k)^(2))* JacobiCD(z, k)+ 2*(k)^(2)* (JacobiCD(z, k))^(3) |
D[JacobiCD[z, (k)^2], {z, 2}]= -(1 + (k)^(2))* JacobiCD[z, (k)^2]+ 2*(k)^(2)* (JacobiCD[z, (k)^2])^(3) |
Successful | Successful | - | - |
| 22.13.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellsdk@{z}{k} = (k^{2}-{k^{\prime}}^{2})\Jacobiellsdk@{z}{k}-2k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{3}@{z}{k}} | diff(JacobiSD(z, k), [z$(2)])=((k)^(2)- 1 - (k)^(2))* JacobiSD(z, k)- 2*(k)^(2)* 1 - (k)^(2)* (JacobiSD(z, k))^(3) |
D[JacobiSD[z, (k)^2], {z, 2}]=((k)^(2)- 1 - (k)^(2))* JacobiSD[z, (k)^2]- 2*(k)^(2)* 1 - (k)^(2)* (JacobiSD[z, (k)^2])^(3) |
Failure | Failure | Fail -1.559655423-5.068856850*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}7.377533436+.6310733818*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}24.14827883+2.560535027*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-1.559655423+5.068856850*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-1.5596554204154063, -5.068856868430466] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.377533435916555, 0.631073384002977] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[24.148278865809726, 2.560535034009612] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.5596554204154063, 5.068856868430466] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellndk@{z}{k} = (1+{k^{\prime}}^{2})\Jacobiellndk@{z}{k}-2{k^{\prime}}^{2}\Jacobiellndk^{3}@{z}{k}} | diff(JacobiND(z, k), [z$(2)])=(1 + 1 - (k)^(2))* JacobiND(z, k)- 21 - (k)^(2)* (JacobiND(z, k))^(3) |
D[JacobiND[z, (k)^2], {z, 2}]=(1 + 1 - (k)^(2))* JacobiND[z, (k)^2]- 21 - (k)^(2)* (JacobiND[z, (k)^2])^(3) |
Failure | Failure | Fail 17.31627209-6.321528171*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}20.48491028+.6948396114*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}2.697171893-16.07884790*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}17.31627209+6.321528171*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[17.316272094007225, -6.32152818402195] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[20.48491028791516, 0.6948396156603991] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.6971717784427156, -16.07884795469416] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[17.316272094007225, 6.32152818402195] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobielldck@{z}{k} = -(1+k^{2})\Jacobielldck@{z}{k}+2\Jacobielldck^{3}@{z}{k}} | diff(JacobiDC(z, k), [z$(2)])= -(1 + (k)^(2))* JacobiDC(z, k)+ 2*(JacobiDC(z, k))^(3) |
D[JacobiDC[z, (k)^2], {z, 2}]= -(1 + (k)^(2))* JacobiDC[z, (k)^2]+ 2*(JacobiDC[z, (k)^2])^(3) |
Successful | Successful | - | - |
| 22.13.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellnck@{z}{k} = (k^{2}-{k^{\prime}}^{2})\Jacobiellnck@{z}{k}+2{k^{\prime}}^{2}\Jacobiellnck^{3}@{z}{k}} | diff(JacobiNC(z, k), [z$(2)])=((k)^(2)- 1 - (k)^(2))* JacobiNC(z, k)+ 21 - (k)^(2)* (JacobiNC(z, k))^(3) |
D[JacobiNC[z, (k)^2], {z, 2}]=((k)^(2)- 1 - (k)^(2))* JacobiNC[z, (k)^2]+ 21 - (k)^(2)* (JacobiNC[z, (k)^2])^(3) |
Failure | Failure | Fail -24.00437993-2.498741953*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-26.57479322-1.960795880*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-31.85910661-.365650073*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-24.00437993+2.498741953*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-24.004379922603327, -2.4987419636935297] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-26.574793224361827, -1.9607958726774548] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-31.85910661323699, -0.36565007186275755] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-24.004379922603327, 2.4987419636935297] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellsck@{z}{k} = (1+{k^{\prime}}^{2})\Jacobiellsck@{z}{k}+2{k^{\prime}}^{2}\Jacobiellsck^{3}@{z}{k}} | diff(JacobiSC(z, k), [z$(2)])=(1 + 1 - (k)^(2))* JacobiSC(z, k)+ 21 - (k)^(2)* (JacobiSC(z, k))^(3) |
D[JacobiSC[z, (k)^2], {z, 2}]=(1 + 1 - (k)^(2))* JacobiSC[z, (k)^2]+ 21 - (k)^(2)* (JacobiSC[z, (k)^2])^(3) |
Failure | Failure | Fail -25.16317836-9.371927930*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}-22.30678436-.748664075*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-21.11933094+.5286047673*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-25.16317836+9.371927930*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-25.16317836015093, -9.371927951109038] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-22.30678435695311, -0.7486640736526304] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-21.119330946363334, 0.5286047645456822] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-25.16317836015093, 9.371927951109038] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellnsk@{z}{k} = -(1+k^{2})\Jacobiellnsk@{z}{k}+2\Jacobiellnsk^{3}@{z}{k}} | diff(JacobiNS(z, k), [z$(2)])= -(1 + (k)^(2))* JacobiNS(z, k)+ 2*(JacobiNS(z, k))^(3) |
D[JacobiNS[z, (k)^2], {z, 2}]= -(1 + (k)^(2))* JacobiNS[z, (k)^2]+ 2*(JacobiNS[z, (k)^2])^(3) |
Successful | Successful | - | - |
| 22.13.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobielldsk@{z}{k} = (k^{2}-{k^{\prime}}^{2})\Jacobielldsk@{z}{k}+2\Jacobielldsk^{3}@{z}{k}} | diff(JacobiDS(z, k), [z$(2)])=((k)^(2)- 1 - (k)^(2))* JacobiDS(z, k)+ 2*(JacobiDS(z, k))^(3) |
D[JacobiDS[z, (k)^2], {z, 2}]=((k)^(2)- 1 - (k)^(2))* JacobiDS[z, (k)^2]+ 2*(JacobiDS[z, (k)^2])^(3) |
Failure | Failure | Fail .1278605556-.9116357015*I <- {z = 2^(1/2)+I*2^(1/2), k = 1}1.564751601-15.92389060*I <- {z = 2^(1/2)+I*2^(1/2), k = 2}-16.64582166-41.94233041*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}.1278605556+.9116357015*I <- {z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[0.1278605552889328, -0.9116357007409521] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.5647516031657338, -15.92389060277217] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-16.645821659513462, -41.94233034981555] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.1278605552889328, 0.9116357007409521] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.13.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellcsk@{z}{k} = (1+{k^{\prime}}^{2})\Jacobiellcsk@{z}{k}+2\Jacobiellcsk^{3}@{z}{k}} | diff(JacobiCS(z, k), [z$(2)])=(1 + 1 - (k)^(2))* JacobiCS(z, k)+ 2*(JacobiCS(z, k))^(3) |
D[JacobiCS[z, (k)^2], {z, 2}]=(1 + 1 - (k)^(2))* JacobiCS[z, (k)^2]+ 2*(JacobiCS[z, (k)^2])^(3) |
Successful | Successful | - | - |
| 22.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellsnk@{x}{k}\diff{x} = k^{-1}\ln@{\Jacobielldnk@{x}{k}-k\Jacobiellcnk@{x}{k}}} | int(JacobiSN(x, k), x)= (k)^(- 1)* ln(JacobiDN(x, k)- k*JacobiCN(x, k)) |
Integrate[JacobiSN[x, (k)^2], x]= (k)^(- 1)* Log[JacobiDN[x, (k)^2]- k*JacobiCN[x, (k)^2]] |
Successful | Failure | - | Successful |
| 22.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellcnk@{x}{k}\diff{x} = k^{-1}\Acos@{\Jacobielldnk@{x}{k}}} | Error |
Integrate[JacobiCN[x, (k)^2], x]= (k)^(- 1)* Integrate[Divide[1, (1-t^2)^(1/2)], {t, JacobiDN[x, (k)^2], 1}] |
Error | Failure | - | Skip |
| 22.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobielldnk@{x}{k}\diff{x} = \Asin@{\Jacobiellsnk@{x}{k}}} | Error |
Integrate[JacobiDN[x, (k)^2], x]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, JacobiSN[x, (k)^2]}] |
Error | Failure | - | Successful |
| 22.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellcdk@{x}{k}\diff{x} = k^{-1}\ln@{\Jacobiellndk@{x}{k}+k\Jacobiellsdk@{x}{k}}} | int(JacobiCD(x, k), x)= (k)^(- 1)* ln(JacobiND(x, k)+ k*JacobiSD(x, k)) |
Integrate[JacobiCD[x, (k)^2], x]= (k)^(- 1)* Log[JacobiND[x, (k)^2]+ k*JacobiSD[x, (k)^2]] |
Successful | Failure | - | Successful |
| 22.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellsdk@{x}{k}\diff{x} = (kk^{\prime})^{-1}\Asin@{-k\Jacobiellcdk@{x}{k}}} | Error |
Integrate[JacobiSD[x, (k)^2], x]=(k*Sqrt[1 - (k)^(2)])^(- 1)* Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, - k*JacobiCD[x, (k)^2]}] |
Error | Failure | - | Skip |
| 22.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellndk@{x}{k}\diff{x} = {k^{\prime}}^{-1}\Acos@{\Jacobiellcdk@{x}{k}}} | Error |
Integrate[JacobiND[x, (k)^2], x]=(Sqrt[1 - (k)^(2)])^(- 1)* Integrate[Divide[1, (1-t^2)^(1/2)], {t, JacobiCD[x, (k)^2], 1}] |
Error | Failure | - | Skip |
| 22.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobielldck@{x}{k}\diff{x} = \ln@{\Jacobiellnck@{x}{k}+\Jacobiellsck@{x}{k}}} | int(JacobiDC(x, k), x)= ln(JacobiNC(x, k)+ JacobiSC(x, k)) |
Integrate[JacobiDC[x, (k)^2], x]= Log[JacobiNC[x, (k)^2]+ JacobiSC[x, (k)^2]] |
Successful | Successful | - | - |
| 22.14.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellnck@{x}{k}\diff{x} = {k^{\prime}}^{-1}\ln@{\Jacobielldck@{x}{k}+k^{\prime}\Jacobiellsck@{x}{k}}} | int(JacobiNC(x, k), x)=(sqrt(1 - (k)^(2)))^(- 1)* ln(JacobiDC(x, k)+sqrt(1 - (k)^(2))*JacobiSC(x, k)) |
Integrate[JacobiNC[x, (k)^2], x]=(Sqrt[1 - (k)^(2)])^(- 1)* Log[JacobiDC[x, (k)^2]+Sqrt[1 - (k)^(2)]*JacobiSC[x, (k)^2]] |
Successful | Successful | - | - |
| 22.14.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellsck@{x}{k}\diff{x} = {k^{\prime}}^{-1}\ln@{\Jacobielldck@{x}{k}+k^{\prime}\Jacobiellnck@{x}{k}}} | int(JacobiSC(x, k), x)=(sqrt(1 - (k)^(2)))^(- 1)* ln(JacobiDC(x, k)+sqrt(1 - (k)^(2))*JacobiNC(x, k)) |
Integrate[JacobiSC[x, (k)^2], x]=(Sqrt[1 - (k)^(2)])^(- 1)* Log[JacobiDC[x, (k)^2]+Sqrt[1 - (k)^(2)]*JacobiNC[x, (k)^2]] |
Successful | Successful | - | - |
| 22.14.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellnsk@{x}{k}\diff{x} = \ln@{\Jacobielldsk@{x}{k}-\Jacobiellcsk@{x}{k}}} | int(JacobiNS(x, k), x)= ln(JacobiDS(x, k)- JacobiCS(x, k)) |
Integrate[JacobiNS[x, (k)^2], x]= Log[JacobiDS[x, (k)^2]- JacobiCS[x, (k)^2]] |
Successful | Successful | - | - |
| 22.14.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobielldsk@{x}{k}\diff{x} = \ln@{\Jacobiellnsk@{x}{k}-\Jacobiellcsk@{x}{k}}} | int(JacobiDS(x, k), x)= ln(JacobiNS(x, k)- JacobiCS(x, k)) |
Integrate[JacobiDS[x, (k)^2], x]= Log[JacobiNS[x, (k)^2]- JacobiCS[x, (k)^2]] |
Successful | Successful | - | - |
| 22.14.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellcsk@{x}{k}\diff{x} = \ln@{\Jacobiellnsk@{x}{k}-\Jacobielldsk@{x}{k}}} | int(JacobiCS(x, k), x)= ln(JacobiNS(x, k)- JacobiDS(x, k)) |
Integrate[JacobiCS[x, (k)^2], x]= Log[JacobiNS[x, (k)^2]- JacobiDS[x, (k)^2]] |
Successful | Successful | - | - |
| 22.14.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\diff{x}}{\Jacobiellsnk@{x}{k}} = \ln@{\frac{\Jacobiellsnk@{x}{k}}{\Jacobiellcnk@{x}{k}+\Jacobielldnk@{x}{k}}}} | int((1)/(JacobiSN(x, k)), x)= ln((JacobiSN(x, k))/(JacobiCN(x, k)+ JacobiDN(x, k))) |
Integrate[Divide[1,JacobiSN[x, (k)^2]], x]= Log[Divide[JacobiSN[x, (k)^2],JacobiCN[x, (k)^2]+ JacobiDN[x, (k)^2]]] |
Successful | Successful | - | - |
| 22.14.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\Jacobiellcnk@{x}{k}\diff{x}}{\Jacobiellsnk@{x}{k}} = \frac{1}{2}\ln@{\frac{1-\Jacobielldnk@{x}{k}}{1+\Jacobielldnk@{x}{k}}}} | int((JacobiCN(x, k))/(JacobiSN(x, k)), x)=(1)/(2)*ln((1 - JacobiDN(x, k))/(1 + JacobiDN(x, k))) |
Integrate[Divide[JacobiCN[x, (k)^2],JacobiSN[x, (k)^2]], x]=Divide[1,2]*Log[Divide[1 - JacobiDN[x, (k)^2],1 + JacobiDN[x, (k)^2]]] |
Failure | Failure | Skip | Fail
Complex[0.6931471805599447, 1.0816575901446905*^-16] <- {Rule[k, 2], Rule[x, 1]}Complex[0.6931471805599456, -3.1415926535897927] <- {Rule[k, 2], Rule[x, 2]}Complex[0.6931471805599457, -3.141592653589793] <- {Rule[k, 2], Rule[x, 3]}Complex[1.098612288668117, 4.781590265396833*^-15] <- {Rule[k, 3], Rule[x, 1]}... skip entries to safe data |
| 22.14.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\Jacobiellcnk@{x}{k}\diff{x}}{\Jacobiellsnk^{2}@{x}{k}} = -\frac{\Jacobielldnk@{x}{k}}{\Jacobiellsnk@{x}{k}}} | int((JacobiCN(x, k))/((JacobiSN(x, k))^(2)), x)= -(JacobiDN(x, k))/(JacobiSN(x, k)) |
Integrate[Divide[JacobiCN[x, (k)^2],(JacobiSN[x, (k)^2])^(2)], x]= -Divide[JacobiDN[x, (k)^2],JacobiSN[x, (k)^2]] |
Successful | Successful | - | - |
| 22.14.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\compellintKk@{k}}\ln@{\Jacobiellsnk@{t}{k}}\diff{t} = -\tfrac{1}{4}\!\ccompellintKk@{k}-\tfrac{1}{2}\!\compellintKk@{k}\ln@@{k}} | int(ln(JacobiSN(t, k)), t = 0..EllipticK(k))= -(1)/(4)*EllipticCK(k)-(1)/(2)*EllipticK(k)*ln(k) |
Integrate[Log[JacobiSN[t, (k)^2]], {t, 0, EllipticK[(k)^2]}]= -Divide[1,4]*EllipticK[1-(k)^2]-Divide[1,2]*EllipticK[(k)^2]*Log[k] |
Failure | Failure | Skip | Successful |
| 22.14.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\compellintKk@{k}}\ln@{\Jacobiellcnk@{t}{k}}\diff{t} = -\tfrac{1}{4}\!\ccompellintKk@{k}+\tfrac{1}{2}\!\compellintKk@{k}\ln@{k^{\prime}/k}} | int(ln(JacobiCN(t, k)), t = 0..EllipticK(k))= -(1)/(4)*EllipticCK(k)+(1)/(2)*EllipticK(k)*ln(sqrt(1 - (k)^(2))/ k) |
Integrate[Log[JacobiCN[t, (k)^2]], {t, 0, EllipticK[(k)^2]}]= -Divide[1,4]*EllipticK[1-(k)^2]+Divide[1,2]*EllipticK[(k)^2]*Log[Sqrt[1 - (k)^(2)]/ k] |
Failure | Failure | Skip | Successful |
| 22.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{\xi}{k} = x} | JacobiSN(xi, k)= x |
JacobiSN[\[Xi], (k)^2]= x |
Failure | Failure | Skip | Fail
Complex[0.11837413740083425, 0.04087130856331978] <- {Rule[k, 1], Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.16253964807069676, 0.7594854905054264] <- {Rule[k, 2], Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.3727323062986447, 0.1514985571826523] <- {Rule[k, 3], Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.11837413740083425, -0.04087130856331978] <- {Rule[k, 1], Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.15.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{\eta}{k} = x} | JacobiCN(eta, k)= x |
JacobiCN[\[Eta], (k)^2]= x |
Failure | Failure | Skip | Fail
Complex[-0.9098721588744132, -0.507161981115838] <- {Rule[k, 1], Rule[x, 1], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.0999336041995775, 0.5782521633446407] <- {Rule[k, 2], Rule[x, 1], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.9421331411733305, -0.059936758566078566] <- {Rule[k, 3], Rule[x, 1], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.9098721588744132, 0.507161981115838] <- {Rule[k, 1], Rule[x, 1], Rule[η, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.15.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{\zeta}{k} = x} | JacobiDN(zeta, k)= x |
JacobiDN[\[zeta], (k)^2]= x |
Failure | Failure | Skip | Error |
| 22.15#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = \aJacobiellsnk@{x}{k}} | xi = InverseJacobiSN(x, k) |
\[Xi]= InverseJacobiSN[x, (k)^2] |
Failure | Failure | Error | Fail
DirectedInfinity[-1] <- {Rule[k, 1], Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8649074180390403, 2.9850098891679915] <- {Rule[k, 1], Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0676399720931227, 2.9850098891679915] <- {Rule[k, 1], Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.571338384966797, 2.492471386122917] <- {Rule[k, 2], Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.15#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = \aJacobiellcnk@{x}{k}} | eta = InverseJacobiCN(x, k) |
\[Eta]= InverseJacobiCN[x, (k)^2] |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {eta = 2^(1/2)+I*2^(1/2), k = 1, x = 1}1.414213562+.367016011*I <- {eta = 2^(1/2)+I*2^(1/2), k = 1, x = 2}1.414213562+.183254145*I <- {eta = 2^(1/2)+I*2^(1/2), k = 1, x = 3}1.414213562+1.414213562*I <- {eta = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[k, 1], Rule[x, 1], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 0.3670160111764975] <- {Rule[k, 1], Rule[x, 2], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 0.1832541450323204] <- {Rule[k, 1], Rule[x, 3], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[k, 2], Rule[x, 1], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.15#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \aJacobielldnk@{x}{k}} | zeta = InverseJacobiDN(x, k) |
\[zeta]= InverseJacobiDN[x, (k)^2] |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {zeta = 2^(1/2)+I*2^(1/2), k = 1, x = 1}1.414213562+.367016011*I <- {zeta = 2^(1/2)+I*2^(1/2), k = 1, x = 2}1.414213562+.183254145*I <- {zeta = 2^(1/2)+I*2^(1/2), k = 1, x = 3}1.414213562+1.414213562*I <- {zeta = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Error |
| 22.15.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -K <= \aJacobiellsnk@{x}{k}} | - EllipticK(k)< = InverseJacobiSN(x, k) |
- EllipticK[(k)^2]< = InverseJacobiSN[x, (k)^2] |
Failure | Failure | Error | Successful |
| 22.15.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsnk@{x}{k} <= K} | InverseJacobiSN(x, k)< = EllipticK(k) |
InverseJacobiSN[x, (k)^2]< = EllipticK[(k)^2] |
Failure | Failure | Error | Successful |
| 22.15.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 <= \aJacobiellcnk@{x}{k}} | 0 < = InverseJacobiCN(x, k) |
0 < = InverseJacobiCN[x, (k)^2] |
Failure | Failure | Successful | Successful |
| 22.15.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcnk@{x}{k} <= 2K} | InverseJacobiCN(x, k)< = 2*EllipticK(k) |
InverseJacobiCN[x, (k)^2]< = 2*EllipticK[(k)^2] |
Failure | Failure | Error | Successful |
| 22.15.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 <= \aJacobielldnk@{x}{k}} | 0 < = InverseJacobiDN(x, k) |
0 < = InverseJacobiDN[x, (k)^2] |
Failure | Failure | Successful | Successful |
| 22.15.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldnk@{x}{k} <= K} | InverseJacobiDN(x, k)< = EllipticK(k) |
InverseJacobiDN[x, (k)^2]< = EllipticK[(k)^2] |
Failure | Failure | Error | Successful |
| 22.15.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = (-1)^{m}\aJacobiellsnk@{x}{k}+2mK} | xi =(- 1)^(m)* InverseJacobiSN(x, k)+ 2*m*K |
\[Xi]=(- 1)^(m)* InverseJacobiSN[x, (k)^2]+ 2*m*K |
Failure | Failure | Error | Skip |
| 22.15.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = +\aJacobiellcnk@{x}{k}+4mK} | eta = + InverseJacobiCN(x, k)+ 4*m*K |
\[Eta]= + InverseJacobiCN[x, (k)^2]+ 4*m*K |
Failure | Failure | Fail -4.242640686-4.242640686*I <- {K = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 1}-4.242640686-5.289838237*I <- {K = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 2}-4.242640686-5.473600103*I <- {K = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 3}-9.899494934-9.899494934*I <- {K = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), k = 1, m = 2, x = 1}... skip entries to safe data |
Skip |
| 22.15.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = -\aJacobiellcnk@{x}{k}+4mK} | eta = - InverseJacobiCN(x, k)+ 4*m*K |
\[Eta]= - InverseJacobiCN[x, (k)^2]+ 4*m*K |
Failure | Failure | Fail -4.242640686-4.242640686*I <- {K = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 1}-4.242640686-3.195443135*I <- {K = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 2}-4.242640686-3.011681269*I <- {K = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 3}-9.899494934-9.899494934*I <- {K = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), k = 1, m = 2, x = 1}... skip entries to safe data |
Skip |
| 22.15.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = +\aJacobielldnk@{x}{k}+2mK} | zeta = + InverseJacobiDN(x, k)+ 2*m*K |
\[zeta]= + InverseJacobiDN[x, (k)^2]+ 2*m*K |
Failure | Failure | Fail -1.414213562-1.414213562*I <- {K = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 1}-1.414213562-2.461411113*I <- {K = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 2}-1.414213562-2.645172979*I <- {K = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 3}-4.242640686-4.242640686*I <- {K = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), k = 1, m = 2, x = 1}... skip entries to safe data |
Error |
| 22.15.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = -\aJacobielldnk@{x}{k}+2mK} | zeta = - InverseJacobiDN(x, k)+ 2*m*K |
\[zeta]= - InverseJacobiDN[x, (k)^2]+ 2*m*K |
Failure | Failure | Fail -1.414213562-1.414213562*I <- {K = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 1}-1.414213562-.367016011*I <- {K = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 2}-1.414213562-.183254145*I <- {K = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), k = 1, m = 1, x = 3}-4.242640686-4.242640686*I <- {K = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), k = 1, m = 2, x = 1}... skip entries to safe data |
Error |
| 22.15.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsnk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}} | InverseJacobiSN(x, k)= int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = 0..x) |
InverseJacobiSN[x, (k)^2]= Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, 0, x}] |
Failure | Failure | Skip | Error |
| 22.15.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})({k^{\prime}}^{2}+k^{2}t^{2})}}} | InverseJacobiCN(x, k)= int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)+ (k)^(2)* (t)^(2)))), t = x..1) |
InverseJacobiCN[x, (k)^2]= Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)+ (k)^(2)* (t)^(2))]], {t, x, 1}] |
Failure | Failure | Skip | Error |
| 22.15.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})(t^{2}-{k^{\prime}}^{2})}}} | InverseJacobiDN(x, k)= int((1)/(sqrt((1 - (t)^(2))*((t)^(2)- 1 - (k)^(2)))), t = x..1) |
InverseJacobiDN[x, (k)^2]= Integrate[Divide[1,Sqrt[(1 - (t)^(2))*((t)^(2)- 1 - (k)^(2))]], {t, x, 1}] |
Error | Failure | - | Error |
| 22.15.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsdk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-{k^{\prime}}^{2}t^{2})(1+k^{2}t^{2})}}} | InverseJacobiSD(x, k)= int((1)/(sqrt((1 - 1 - (k)^(2)* (t)^(2))*(1 + (k)^(2)* (t)^(2)))), t = 0..x) |
InverseJacobiSD[x, (k)^2]= Integrate[Divide[1,Sqrt[(1 - 1 - (k)^(2)* (t)^(2))*(1 + (k)^(2)* (t)^(2))]], {t, 0, x}] |
Error | Failure | - | Successful |
| 22.15.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellndk@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(1-{k^{\prime}}^{2}t^{2})}}} | InverseJacobiND(x, k)= int((1)/(sqrt(((t)^(2)- 1)*(1 - 1 - (k)^(2)* (t)^(2)))), t = 1..x) |
InverseJacobiND[x, (k)^2]= Integrate[Divide[1,Sqrt[((t)^(2)- 1)*(1 - 1 - (k)^(2)* (t)^(2))]], {t, 1, x}] |
Failure | Failure | Skip | Successful |
| 22.15.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellnck@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(k^{2}+{k^{\prime}}^{2}t^{2})}}} | InverseJacobiNC(x, k)= int((1)/(sqrt(((t)^(2)- 1)*((k)^(2)+ 1 - (k)^(2)* (t)^(2)))), t = 1..x) |
InverseJacobiNC[x, (k)^2]= Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((k)^(2)+ 1 - (k)^(2)* (t)^(2))]], {t, 1, x}] |
Failure | Failure | Skip | Error |
| 22.15.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsck@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1+t^{2})(1+{k^{\prime}}^{2}t^{2})}}} | InverseJacobiSC(x, k)= int((1)/(sqrt((1 + (t)^(2))*(1 + 1 - (k)^(2)* (t)^(2)))), t = 0..x) |
InverseJacobiSC[x, (k)^2]= Integrate[Divide[1,Sqrt[(1 + (t)^(2))*(1 + 1 - (k)^(2)* (t)^(2))]], {t, 0, x}] |
Failure | Failure | Skip | Error |
| 22.15.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellnsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}}} | InverseJacobiNS(x, k)= int((1)/(sqrt(((t)^(2)- 1)*((t)^(2)- (k)^(2)))), t = x..infinity) |
InverseJacobiNS[x, (k)^2]= Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((t)^(2)- (k)^(2))]], {t, x, Infinity}] |
Failure | Failure | Skip | Error |
| 22.15.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}+k^{2})(t^{2}-{k^{\prime}}^{2})}}} | InverseJacobiDS(x, k)= int((1)/(sqrt(((t)^(2)+ (k)^(2))*((t)^(2)- 1 - (k)^(2)))), t = x..infinity) |
InverseJacobiDS[x, (k)^2]= Integrate[Divide[1,Sqrt[((t)^(2)+ (k)^(2))*((t)^(2)- 1 - (k)^(2))]], {t, x, Infinity}] |
Error | Failure | - | Error |
| 22.15.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(1+t^{2})(t^{2}+{k^{\prime}}^{2})}}} | InverseJacobiCS(x, k)= int((1)/(sqrt((1 + (t)^(2))*((t)^(2)+ 1 - (k)^(2)))), t = x..infinity) |
InverseJacobiCS[x, (k)^2]= Integrate[Divide[1,Sqrt[(1 + (t)^(2))*((t)^(2)+ 1 - (k)^(2))]], {t, x, Infinity}] |
Failure | Failure | Skip | Error |
| 22.16.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x+2K}{k} = \Jacobiamk@{x}{k}+\pi} | JacobiAM(x + 2*EllipticK(k), k)= JacobiAM(x, k)+ Pi |
Error |
Failure | Error | Error | - |
| 22.16.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{k} = \int_{0}^{x}\Jacobielldnk@{t}{k}\diff{t}} | JacobiAM(x, k)= int(JacobiDN(t, k), t = 0..x) |
Error |
Failure | Error | Skip | - |
| 22.16.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{0} = x} | JacobiAM(x, 0)= x |
Error |
Successful | Error | - | - |
| 22.16.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{1} = \Gudermannian@{x}} | JacobiAM(x, 1)= arctan(sinh(x)) |
Error |
Failure | Error | Successful | - |
| 22.16.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{k} = \frac{\pi}{2K}x+2\sum_{n=1}^{\infty}\frac{q^{n}\sin@{2n\zeta}}{n(1+q^{2n})}} | JacobiAM(x, k)=(Pi)/(2*EllipticK(k))*x + 2*sum(((q)^(n)* sin(2*n*zeta))/(n*(1 + (q)^(2*n))), n = 1..infinity) |
Error |
Failure | Error | Skip | - |
| 22.16.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \incellintFk@{\phi}{k}} | x = EllipticF(sin(phi), k) |
x = EllipticF[\[Phi], (k)^2] |
Failure | Failure | Fail .5109255834-1.490381835*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 1}1.510925583-1.490381835*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 2}2.510925583-1.490381835*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 3}.7620067201-1.041441678*I <- {phi = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Fail
Complex[0.5109255837122914, -1.4903818357543746] <- {Rule[k, 1], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.5109255837122912, -1.4903818357543746] <- {Rule[k, 1], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.5109255837122912, -1.4903818357543746] <- {Rule[k, 1], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.762006720261616, -1.0414416780368256] <- {Rule[k, 2], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.16.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{k} = \phi} | JacobiAM(x, k)= phi |
Error |
Failure | Error | Fail -.548444079-1.414213562*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 1}-.112453227-1.414213562*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 2}.57090779e-1-1.414213562*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 3}-.9119062827-1.414213562*I <- {phi = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
- |
| 22.16.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{x}{k} = \sin@@{\phi}} | JacobiSN(x, k)= sin(phi) |
JacobiSN[x, (k)^2]= Sin[\[Phi]] |
Failure | Failure | Fail -1.389941384-.3017614705*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 1}-1.187507960-.3017614705*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 2}-1.156480786-.3017614705*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 3}-1.670086451-.3017614705*I <- {phi = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Fail
Complex[-1.3899413853835214, -0.30176146986776087] <- {Rule[k, 1], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.1875079612634694, -0.30176146986776087] <- {Rule[k, 1], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.1564807876525558, -0.30176146986776087] <- {Rule[k, 1], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6700864525401473, -0.3017614698677609] <- {Rule[k, 2], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.16.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\phi} = \sin@{\Jacobiamk@{x}{k}}} | sin(phi)= sin(JacobiAM(x, k)) |
Error |
Failure | Error | Fail 1.389941384+.3017614705*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 1}1.187507960+.3017614705*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 2}1.156480786+.3017614705*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 3}1.670086451+.3017614705*I <- {phi = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
- |
| 22.16.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{x}{k} = \cos@@{\phi}} | JacobiCN(x, k)= cos(phi) |
JacobiCN[x, (k)^2]= Cos[\[Phi]] |
Failure | Failure | Fail .3083802813+1.911393109*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 1}-.738717636e-1+1.911393109*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 2}-.2403460650+1.911393109*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 3}.5368000659+1.911393109*I <- {phi = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Fail
Complex[0.3083802819691609, 1.9113931101642103] <- {Rule[k, 1], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.07387176286064484, 1.9113931101642103] <- {Rule[k, 1], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.24034606427529137, 1.9113931101642103] <- {Rule[k, 1], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5368000666176019, 1.9113931101642103] <- {Rule[k, 2], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.16.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\phi} = \cos@{\Jacobiamk@{x}{k}}} | cos(phi)= cos(JacobiAM(x, k)) |
Error |
Failure | Error | Fail -.3083802813-1.911393109*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 1}.738717636e-1-1.911393109*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 2}.2403460650-1.911393109*I <- {phi = 2^(1/2)+I*2^(1/2), k = 1, x = 3}-.5368000659-1.911393109*I <- {phi = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
- |
| 22.16.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \JacobiZetak@{x+K}{k} = \JacobiZetak@{x}{k}-k^{2}\Jacobiellsnk@{x}{k}\Jacobiellcdk@{x}{k}} | JacobiZeta(x + EllipticK(k), k)= JacobiZeta(x, k)- (k)^(2)* JacobiSN(x, k)*JacobiCD(x, k) |
JacobiZeta[x + EllipticK[(k)^2], k]= JacobiZeta[x, k]- (k)^(2)* JacobiSN[x, (k)^2]*JacobiCD[x, (k)^2] |
Failure | Failure | Error | Fail
Complex[-9.092646035261055, 0.7547542476789773] <- {Rule[k, 2], Rule[x, 1]}Complex[0.5691890271397613, -1.7224198606648595] <- {Rule[k, 2], Rule[x, 2]}Complex[-0.6254417826653399, -1.1984364919906034] <- {Rule[k, 2], Rule[x, 3]}Complex[0.24923293591578033, 0.8848347496931445] <- {Rule[k, 3], Rule[x, 1]}... skip entries to safe data |
| 22.16.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \JacobiZetak@{x+2K}{k} = \JacobiZetak@{x}{k}} | JacobiZeta(x + 2*EllipticK(k), k)= JacobiZeta(x, k) |
JacobiZeta[x + 2*EllipticK[(k)^2], k]= JacobiZeta[x, k] |
Successful | Failure | - | Fail
Complex[-3.520658209011301, -4.348209951262927] <- {Rule[k, 2], Rule[x, 1]}Complex[2.8383377769721507, -5.069497738677276] <- {Rule[k, 2], Rule[x, 2]}Complex[5.651309663980639, 0.2964137811420908] <- {Rule[k, 2], Rule[x, 3]}Complex[-5.093513410963294, -0.873054809617268] <- {Rule[k, 3], Rule[x, 1]}... skip entries to safe data |
| 22.17.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}} | genJacobiellk(p)*q* z*k = genJacobiellk(p)*q* z- k |
genJacobiellk(p)*q* z*k = genJacobiellk(p)*q* z- k |
Failure | Failure | Error | Skip |
| 22.17.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}} | JacobiSN(z, 1/ k)= k*JacobiSN(z/ k, k) |
JacobiSN[z, (1/ k)^2]= k*JacobiSN[z/ k, (k)^2] |
Failure | Failure | Successful | Successful |
| 22.17.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}} | JacobiCN(z, 1/ k)= JacobiDN(z/ k, k) |
JacobiCN[z, (1/ k)^2]= JacobiDN[z/ k, (k)^2] |
Failure | Failure | Successful | Successful |
| 22.17.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}} | JacobiDN(z, 1/ k)= JacobiCN(z/ k, k) |
JacobiDN[z, (1/ k)^2]= JacobiCN[z/ k, (k)^2] |
Failure | Failure | Successful | Successful |
| 22.17.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{ik} = k^{\prime}_{1}\Jacobiellsdk@{z/k^{\prime}_{1}}{k_{1}}} | JacobiSN(z, I*k)=sqrt(1 - (k)^(2))[1]*JacobiSD(z/sqrt(1 - (k)^(2))[1], k[1]) |
JacobiSN[z, (I*k)^2]=Subscript[Sqrt[1 - (k)^(2)], 1]*JacobiSD[z/Subscript[Sqrt[1 - (k)^(2)], 1], (Subscript[k, 1])^2] |
Failure | Failure | Error | Successful |
| 22.17.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{ik} = \Jacobiellcdk@{z/k^{\prime}_{1}}{k_{1}}} | JacobiCN(z, I*k)= JacobiCD(z/sqrt(1 - (k)^(2))[1], k[1]) |
JacobiCN[z, (I*k)^2]= JacobiCD[z/Subscript[Sqrt[1 - (k)^(2)], 1], (Subscript[k, 1])^2] |
Failure | Failure | Error | Successful |
| 22.17.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{ik} = \Jacobiellndk@{z/k^{\prime}_{1}}{k_{1}}} | JacobiDN(z, I*k)= JacobiND(z/sqrt(1 - (k)^(2))[1], k[1]) |
JacobiDN[z, (I*k)^2]= JacobiND[z/Subscript[Sqrt[1 - (k)^(2)], 1], (Subscript[k, 1])^2] |
Failure | Failure | Error | Successful |
| 22.18#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = a\Jacobiellsnk@{u}{k}} | x = a*JacobiSN(u, k) |
x = a*JacobiSN[u, (k)^2] |
Failure | Failure | Fail -.523819113-1.639420631*I <- {a = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), k = 1, x = 1}.476180887-1.639420631*I <- {a = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), k = 1, x = 2}1.476180887-1.639420631*I <- {a = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), k = 1, x = 3}.8897268907-2.258422469*I <- {a = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Skip |
| 22.18#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = b\Jacobiellcnk@{u}{k}} | y = b*JacobiCN(u, k) |
y = b*JacobiCN[u, (k)^2] |
Failure | Failure | Fail .1553046323+.5897753365*I <- {b = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), k = 1, y = 1}1.155304632+.5897753365*I <- {b = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), k = 1, y = 2}2.155304632+.5897753365*I <- {b = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), k = 1, y = 3}3.373313072+.7377689657*I <- {b = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), k = 2, y = 1}... skip entries to safe data |
Skip |
| 22.18.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle l(r) = (1/\sqrt{2})\aJacobiellcnk@{r}{1/\sqrt{2}}} | l*(r)=(1/sqrt(2))* InverseJacobiCN(r, 1/sqrt(2)) |
l*(r)=(1/Sqrt[2])* InverseJacobiCN[r, (1/Sqrt[2])^2] |
Failure | Failure | Fail 1.062814328+2.373843104*I <- {r = 2^(1/2)+I*2^(1/2), l = 1}2.477027890+3.788056666*I <- {r = 2^(1/2)+I*2^(1/2), l = 2}3.891241452+5.202270228*I <- {r = 2^(1/2)+I*2^(1/2), l = 3}1.062814328-2.373843104*I <- {r = 2^(1/2)-I*2^(1/2), l = 1}... skip entries to safe data |
Fail
Complex[1.0628143278928741, 2.3738431050389313] <- {Rule[l, 1], Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.4770278902659695, 3.788056667412026] <- {Rule[l, 2], Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.891241452639065, 5.202270229785122] <- {Rule[l, 3], Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0628143278928741, -2.3738431050389313] <- {Rule[l, 1], Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.18.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}} | r = JacobiCN(sqrt(2)*l, 1/sqrt(2)) |
r = JacobiCN[Sqrt[2]*l, (1/Sqrt[2])^2] |
Failure | Failure | Fail 1.103475632+1.414213562*I <- {r = 2^(1/2)+I*2^(1/2), l = 1}2.087946761+1.414213562*I <- {r = 2^(1/2)+I*2^(1/2), l = 2}2.280767714+1.414213562*I <- {r = 2^(1/2)+I*2^(1/2), l = 3}1.103475632-1.414213562*I <- {r = 2^(1/2)-I*2^(1/2), l = 1}... skip entries to safe data |
Fail
Complex[1.103475632039239, 1.4142135623730951] <- {Rule[l, 1], Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.087946761347629, 1.4142135623730951] <- {Rule[l, 2], Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.280767714220744, 1.4142135623730951] <- {Rule[l, 3], Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.103475632039239, -1.4142135623730951] <- {Rule[l, 1], Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.18#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}\Jacobielldnk@{\sqrt{2}l}{1/\sqrt{2}}} | x = JacobiCN(sqrt(2)*l, 1/sqrt(2))*JacobiDN(sqrt(2)*l, 1/sqrt(2)) |
x = JacobiCN[Sqrt[2]*l, (1/Sqrt[2])^2]*JacobiDN[Sqrt[2]*l, (1/Sqrt[2])^2] |
Failure | Failure | Fail .7699114076 <- {l = 1, x = 1}1.769911408 <- {l = 1, x = 2}2.769911408 <- {l = 1, x = 3}1.574437352 <- {l = 2, x = 1}... skip entries to safe data |
Fail
Complex[0.7699114077583536, 0.0] <- {Rule[l, 1], Rule[x, 1]}Complex[1.7699114077583538, 0.0] <- {Rule[l, 1], Rule[x, 2]}Complex[2.7699114077583538, 0.0] <- {Rule[l, 1], Rule[x, 3]}Complex[1.574437352038115, 0.0] <- {Rule[l, 2], Rule[x, 1]}... skip entries to safe data |
| 22.19.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{\theta(t)}{t} = -\sin@@{\theta(t)}} | diff(theta*(t), [t$(2)])= - sin(theta*(t)) |
D[\[Theta]*(t), {t, 2}]= - Sin[\[Theta]*(t)] |
Failure | Failure | Fail 0.+27.28991714*I <- {t = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}-.7568024940+0.*I <- {t = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}0.-27.28991714*I <- {t = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}.7568024940+0.*I <- {t = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.0, 27.28991719712775] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-0.7568024953079282 <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -27.28991719712775] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}0.7568024953079282 <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.19.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\tfrac{1}{2}\theta(t)} = \sin@{\frac{1}{2}\alpha}\Jacobiellsnk@{t+K}{\sin@{\tfrac{1}{2}\alpha}}} | sin((1)/(2)*theta*(t))= sin((1)/(2)*alpha)*JacobiSN(t + EllipticK(k), sin((1)/(2)*alpha)) |
Sin[Divide[1,2]*\[Theta]*(t)]= Sin[Divide[1,2]*\[Alpha]]*JacobiSN[t + EllipticK[(k)^2], (Sin[Divide[1,2]*\[Alpha]])^2] |
Failure | Failure | Error | Skip |
| 22.19.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta(t) = 2\Jacobiamk@{t\sqrt{E/2}}{\sqrt{2/E}}} | theta*(t)= 2*JacobiAM(t*sqrt(E/ 2), sqrt(2/ E)) |
Error |
Failure | Error | Fail -2.607335908+2.693048555*I <- {E = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}1.392664090-1.306951443*I <- {E = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}-2.607335908-5.306951441*I <- {E = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}-6.607335906-1.306951443*I <- {E = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
- |
| 22.19.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{x(t)}{t} = -\deriv{V(x)}{x}} | diff(x*(t), [t$(2)])= - diff(V*(x), x) |
D[x*(t), {t, 2}]= - D[V*(x), x] |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {V = 2^(1/2)+I*2^(1/2)}1.414213562-1.414213562*I <- {V = 2^(1/2)-I*2^(1/2)}-1.414213562-1.414213562*I <- {V = -2^(1/2)-I*2^(1/2)}-1.414213562+1.414213562*I <- {V = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 22.19.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(t) = a\Jacobiellcnk@{t\sqrt{1+2\eta}}{k}} | x*(t)= a*JacobiCN(t*sqrt(1 + 2*eta), k) |
x*(t)= a*JacobiCN[t*Sqrt[1 + 2*\[Eta]], (k)^2] |
Failure | Failure | Fail 1.973069551+1.442641289*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 1}3.387283113+2.856854851*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 2}4.801496675+4.271068413*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 3}.191022968-.212139835*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Skip |
| 22.19.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(t) = a\Jacobiellsnk@{t\sqrt{1-\eta}}{k}} | x*(t)= a*JacobiSN(t*sqrt(1 - eta), k) |
x*(t)= a*JacobiSN[t*Sqrt[1 - \[Eta]], (k)^2] |
Failure | Failure | Fail .3281638e-2+.32333204e-1*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 1}1.417495200+1.446546766*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 2}2.831708762+2.860760328*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 3}2.320220885+2.141378505*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Skip |
| 22.19.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(t) = a\Jacobielldnk@{t\sqrt{\eta}}{k}} | x*(t)= a*JacobiDN(t*sqrt(eta), k) |
x*(t)= a*JacobiDN[t*Sqrt[\[Eta]], (k)^2] |
Failure | Failure | Fail 1.853632511+2.613297406*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 1}3.267846073+4.027510968*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 2}4.682059635+5.441724530*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 3}1.885012698-.421765357*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Skip |
| 22.19.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(t) = a\Jacobiellcnk@{t\sqrt{2\eta-1}}{k}} | x*(t)= a*JacobiCN(t*sqrt(2*eta - 1), k) |
x*(t)= a*JacobiCN[t*Sqrt[2*\[Eta]- 1], (k)^2] |
Failure | Failure | Fail 2.558292975+2.017654962*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 1}3.972506537+3.431868524*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 2}5.386720099+4.846082086*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 1, x = 3}.335387665+1.074384225*I <- {a = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Skip |
| 22.20.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi_{n-1} = \frac{1}{2}\left(\phi_{n}+\asin@{\frac{c_{n}}{a_{n}}\sin@@{\phi_{n}}}\right)} | phi[n - 1]=(1)/(2)*(phi[n]+ arcsin((c[n])/(a[n])*sin(phi[n]))) |
Subscript[\[Phi], n - 1]=Divide[1,2]*(Subscript[\[Phi], n]+ ArcSin[Divide[Subscript[c, n],Subscript[a, n]]*Sin[Subscript[\[Phi], n]]]) |
Failure | Failure | Fail -2.828427124*I <- {a[n] = 2^(1/2)+I*2^(1/2), c[n] = 2^(1/2)+I*2^(1/2), phi[n] = 2^(1/2)+I*2^(1/2), phi[n-1] = 2^(1/2)-I*2^(1/2)}-2.828427124-2.828427124*I <- {a[n] = 2^(1/2)+I*2^(1/2), c[n] = 2^(1/2)+I*2^(1/2), phi[n] = 2^(1/2)+I*2^(1/2), phi[n-1] = -2^(1/2)-I*2^(1/2)}-2.828427124 <- {a[n] = 2^(1/2)+I*2^(1/2), c[n] = 2^(1/2)+I*2^(1/2), phi[n] = 2^(1/2)+I*2^(1/2), phi[n-1] = -2^(1/2)+I*2^(1/2)}2.828427124*I <- {a[n] = 2^(1/2)+I*2^(1/2), c[n] = 2^(1/2)+I*2^(1/2), phi[n] = 2^(1/2)-I*2^(1/2), phi[n-1] = 2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.0, 2.8284271247461903] <- {Rule[Subscript[a, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[c, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, Plus[-1, n]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, n], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[Subscript[a, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[c, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, Plus[-1, n]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, n], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}2.8284271247461903 <- {Rule[Subscript[a, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[c, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, Plus[-1, n]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, n], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -2.8284271247461903] <- {Rule[Subscript[a, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[c, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, Plus[-1, n]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[ϕ, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.20#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{x}{k} = \sin@@{\phi_{0}}} | JacobiSN(x, k)= sin(phi[0]) |
JacobiSN[x, (k)^2]= Sin[Subscript[\[Phi], 0]] |
Failure | Failure | Fail -1.389941384-.3017614705*I <- {phi[0] = 2^(1/2)+I*2^(1/2), k = 1, x = 1}-1.187507960-.3017614705*I <- {phi[0] = 2^(1/2)+I*2^(1/2), k = 1, x = 2}-1.156480786-.3017614705*I <- {phi[0] = 2^(1/2)+I*2^(1/2), k = 1, x = 3}-1.670086451-.3017614705*I <- {phi[0] = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Fail
Complex[-1.3899413853835214, -0.30176146986776087] <- {Rule[k, 1], Rule[x, 1], Rule[Subscript[ϕ, 0], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.1875079612634694, -0.30176146986776087] <- {Rule[k, 1], Rule[x, 2], Rule[Subscript[ϕ, 0], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.1564807876525558, -0.30176146986776087] <- {Rule[k, 1], Rule[x, 3], Rule[Subscript[ϕ, 0], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6700864525401473, -0.3017614698677609] <- {Rule[k, 2], Rule[x, 1], Rule[Subscript[ϕ, 0], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.20#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{x}{k} = \cos@@{\phi_{0}}} | JacobiCN(x, k)= cos(phi[0]) |
JacobiCN[x, (k)^2]= Cos[Subscript[\[Phi], 0]] |
Failure | Failure | Fail .3083802813+1.911393109*I <- {phi[0] = 2^(1/2)+I*2^(1/2), k = 1, x = 1}-.738717636e-1+1.911393109*I <- {phi[0] = 2^(1/2)+I*2^(1/2), k = 1, x = 2}-.2403460650+1.911393109*I <- {phi[0] = 2^(1/2)+I*2^(1/2), k = 1, x = 3}.5368000659+1.911393109*I <- {phi[0] = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
Fail
Complex[0.3083802819691609, 1.9113931101642103] <- {Rule[k, 1], Rule[x, 1], Rule[Subscript[ϕ, 0], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.07387176286064484, 1.9113931101642103] <- {Rule[k, 1], Rule[x, 2], Rule[Subscript[ϕ, 0], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.24034606427529137, 1.9113931101642103] <- {Rule[k, 1], Rule[x, 3], Rule[Subscript[ϕ, 0], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5368000666176019, 1.9113931101642103] <- {Rule[k, 2], Rule[x, 1], Rule[Subscript[ϕ, 0], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 22.20#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{x}{k} = \frac{\cos@@{\phi_{0}}}{\cos@{\phi_{1}-\phi_{0}}}} | JacobiDN(x, k)=(cos(phi[0]))/(cos(phi[1]- phi[0])) |
JacobiDN[x, (k)^2]=Divide[Cos[Subscript[\[Phi], 0]],Cos[Subscript[\[Phi], 1]- Subscript[\[Phi], 0]]] |
Failure | Failure | Fail .3083802813+1.911393109*I <- {phi[0] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 1, x = 1}-.738717636e-1+1.911393109*I <- {phi[0] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 1, x = 2}-.2403460650+1.911393109*I <- {phi[0] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 1, x = 3}-.6095389579+1.911393109*I <- {phi[0] = 2^(1/2)+I*2^(1/2), phi[1] = 2^(1/2)+I*2^(1/2), k = 2, x = 1}... skip entries to safe data |
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