DLMF:19.4.E7 (Q6127): Difference between revisions

Revision as of 13:37, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:19.4.E7	No description defined

{\displaystyle{\displaystyle\frac{\partial\Pi\left(\phi,\alpha^{2},k\right)}{% \partial k}=\frac{k}{{k^{\prime}}^{2}(k^{2}-\alpha^{2})}\left({E\left(\phi,k% \right)-{k^{\prime}}^{2}\Pi\left(\phi,\alpha^{2},k\right)}-\frac{k^{2}\sin\phi% \cos\phi}{\sqrt{1-k^{2}{\sin^{2}}\phi}}\right).}}

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DLMF:19.4.E7

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{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2aadec

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

C19.S2.E5.m2abdec

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{\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}% \right)}}

C19.S2.E7.m2adec

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@@ Property / Symbols used @@
+Legendre’s incomplete elliptic integral of the third kind
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}% \right)}}$ 
\incellintPik@{\NVar{\phi}}{\NVar{\alpha}^{2}}{\NVar{k}}
+xml-id: C19.S2.E7.m2adec