@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\phi=\operatorname{arcsin}\sqrt{2/(q+1)}=% \operatorname{arccos}\left(\tan\theta\right)}}$ 
\phi=\asin@@{\sqrt{2/(q+1)}}=\acos@{\tan@@{\theta}}
+Normal rank
@@ Property / Symbols used @@
+Legendre’s incomplete elliptic integral of the first kind
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}$ 
\incellintFk@{\NVar{\phi}}{\NVar{k}}
+xml-id: C19.S2.E4.m2aadec
@@ Property / Symbols used @@
+Q11208
@@ Property / Symbols used: Q11208 / rank @@
+Normal rank
@@ Property / Symbols used: Q11208 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}$ 
\acos@@{\NVar{z}}
@@ Property / Symbols used: Q11208 / qualifier @@
+xml-id: C4.S23.SS2.p1.m6adec
@@ Property / Symbols used @@
+Q11242
@@ Property / Symbols used: Q11242 / rank @@
+Normal rank
@@ Property / Symbols used: Q11242 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}$ 
\asin@@{\NVar{z}}
@@ Property / Symbols used: Q11242 / qualifier @@
+xml-id: C4.S23.SS2.p1.m5adec
@@ Property / Symbols used @@
+tangent function
@@ Property / Symbols used: tangent function / rank @@
+Normal rank
@@ Property / Symbols used: tangent function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\tan\NVar{z}}}$ 
\tan@@{\NVar{z}}
@@ Property / Symbols used: tangent function / qualifier @@
+xml-id: C4.S14.E4.m2adec
@@ Property / Symbols used @@
+Q11807
@@ Property / Symbols used: Q11807 / rank @@
+Normal rank
@@ Property / Symbols used: Q11807 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\phi}}$ 
\phi
@@ Property / Symbols used: Q11807 / qualifier @@
+xml-id: C19.S1.XMD4.m1edec
@@ Property / Symbols used @@
+Q11919
@@ Property / Symbols used: Q11919 / rank @@
+Normal rank
@@ Property / Symbols used: Q11919 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle q}}$ 
q
@@ Property / Symbols used: Q11919 / qualifier @@
+xml-id: C19.S30.XMD5.m1adec
@@ Property / Symbols used @@
+Q11920
@@ Property / Symbols used: Q11920 / rank @@
+Normal rank
@@ Property / Symbols used: Q11920 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle s}}$ 
s
@@ Property / Symbols used: Q11920 / qualifier @@
+xml-id: C19.S30.XMD6.m1adec

DLMF:19.30.E12 (Q6687): Difference between revisions

ϕ = arcsin ⁡ 2 / ( q + 1 ) = arccos ⁡ ( tan ⁡ θ ) italic-ϕ 2 𝑞 1 𝜃 {\displaystyle{\displaystyle\phi=\operatorname{arcsin}\sqrt{2/(q+1)}=% \operatorname{arccos}\left(\tan\theta\right)}}

F ⁡ ( ϕ , k ) elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}

arccos ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}

arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}

tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

q 𝑞 {\displaystyle{\displaystyle q}}

s 𝑠 {\displaystyle{\displaystyle s}}

Latest revision as of 14:23, 2 January 2020

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${\displaystyle{\displaystyle\phi=\operatorname{arcsin}\sqrt{2/(q+1)}=% \operatorname{arccos}\left(\tan\theta\right)}}$

${\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}$

${\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}$

${\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}$

${\displaystyle{\displaystyle\tan\NVar{z}}}$

${\displaystyle{\displaystyle\phi}}$

${\displaystyle{\displaystyle q}}$

${\displaystyle{\displaystyle s}}$