DLMF:29.5.E5 (Q8623): Difference between revisions

Revision as of 15:45, 2 January 2020

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English	DLMF:29.5.E5	No description defined

{\displaystyle{\displaystyle{\lim_{k\to 1-}\frac{\mathit{Ec}^{m}_{\nu}\left(z,% k^{2}\right)}{\mathit{Ec}^{m}_{\nu}\left(0,k^{2}\right)}=\lim_{k\to 1-}\frac{% \mathit{Es}^{m+1}_{\nu}\left(z,k^{2}\right)}{\mathit{Es}^{m+1}_{\nu}\left(0,k^% {2}\right)}}=\frac{1}{(\cosh z)^{\mu}}F\left({\tfrac{1}{2}\mu-\tfrac{1}{2}\nu,% \tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}\atop\tfrac{1}{2}};{\tanh^{2}}z% \right),}}

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DLMF:29.5.E5

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{\displaystyle{\displaystyle m}}

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{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}

C15.S2.E1.m2adec

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@@ Property / Symbols used @@
+$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$  Gauss’ hypergeometric function
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$ 
\hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
+xml-id: C15.S2.E1.m2adec