DLMF:22.6.E4 (Q6938): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellcdk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E8.m2adec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

nd ⁡ ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellndk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E6.m3adec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

sd ⁡ ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellsdk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E7.m2adec
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11988 / rank
 
Normal rank
Property / Symbols used: Q11988 / qualifier
 
Defining formula:

k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11988 / qualifier
 
xml-id: C22.S1.XMD5.m1adec

Latest revision as of 14:57, 2 January 2020

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DLMF:22.6.E4
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    Statements

    Defining formula
    - k 2 ⁢ k ′ 2 ⁢ sd 2 ⁡ ( z , k ) = k 2 ⁢ ( cd 2 ⁡ ( z , k ) - 1 ) = k ′ 2 ⁢ ( 1 - nd 2 ⁡ ( z , k ) ) . superscript 𝑘 2 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sd 2 𝑧 𝑘 superscript 𝑘 2 Jacobi-elliptic-cd 2 𝑧 𝑘 1 superscript superscript 𝑘 ′ 2 1 Jacobi-elliptic-nd 2 𝑧 𝑘 {\displaystyle{\displaystyle-k^{2}{k^{\prime}}^{2}{\operatorname{sd}^{2}}\left% (z,k\right)=k^{2}({\operatorname{cd}^{2}}\left(z,k\right)-1)={k^{\prime}}^{2}(% 1-{\operatorname{nd}^{2}}\left(z,k\right)).}}
    0 references
    DLMF id
    DLMF:22.6.E4
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m2adec
    0 references
    Jacobian elliptic function
    Defining formula
    nd ⁡ ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m3adec
    0 references
    Jacobian elliptic function
    Defining formula
    sd ⁡ ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m2adec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1cdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1cdec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1adec
    0 references
     
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