DLMF:19.2.E6 (Q6087): Difference between revisions

Revision as of 13:35, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:19.2.E6	No description defined

{\displaystyle{\displaystyle D\left(\phi,k\right)=\int_{0}^{\phi}\frac{{\sin^{% 2}}\theta\mathrm{d}\theta}{\sqrt{1-k^{2}{\sin^{2}}\theta}}=\int_{0}^{\sin\phi}% \frac{t^{2}\mathrm{d}t}{\sqrt{1-t^{2}}\sqrt{1-k^{2}t^{2}}}=(F\left(\phi,k% \right)-E\left(\phi,k\right))/k^{2}.}}

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DLMF:19.2.E6

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{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1addec

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

C19.S2.E4.m2aadec

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

C19.S2.E5.m2aadec

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@@ Property / Symbols used @@
+Legendre’s incomplete elliptic integral of the second kind
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}$ 
\incellintEk@{\NVar{\phi}}{\NVar{k}}
+xml-id: C19.S2.E5.m2aadec