DLMF:19.5.E2 (Q6131): Difference between revisions

Revision as of 13:39, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:19.5.E2	No description defined

{\displaystyle{\displaystyle E\left(k\right)=\frac{\pi}{2}\sum_{m=0}^{\infty}% \frac{{\left(-\tfrac{1}{2}\right)_{m}}{\left(\tfrac{1}{2}\right)_{m}}}{m!\;m!}% k^{2m}=\frac{\pi}{2}{{}_{2}F_{1}}\left(-\tfrac{1}{2},\tfrac{1}{2};1;k^{2}% \right),}}

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DLMF:19.5.E2

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{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

C16.S2.m5aadec

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{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1aadec

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@@ Property / Symbols used @@
+Q10759
@@ Property / Symbols used: Q10759 / rank @@
+Normal rank
@@ Property / Symbols used: Q10759 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$ 
\Pochhammersym{\NVar{a}}{\NVar{n}}
@@ Property / Symbols used: Q10759 / qualifier @@
+xml-id: C5.S2.SS3.m1aadec