DLMF:19.2.E5 (Q6086): Difference between revisions

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Property / Symbols defined: Legendre’s incomplete elliptic integral of the second kind / rank
 
Normal rank

Revision as of 15:22, 30 December 2019

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DLMF:19.2.E5
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    E ( ϕ , k ) = 0 ϕ 1 - k 2 sin 2 θ d θ = 0 sin ϕ 1 - k 2 t 2 1 - t 2 d t . elliptic-integral-second-kind-E italic-ϕ 𝑘 superscript subscript 0 italic-ϕ 1 superscript 𝑘 2 2 𝜃 𝜃 superscript subscript 0 italic-ϕ 1 superscript 𝑘 2 superscript 𝑡 2 1 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle E\left(\phi,k\right)=\int_{0}^{\phi}\sqrt{1-k^{2}% {\sin^{2}}\theta}\mathrm{d}\theta\\ =\int_{0}^{\sin\phi}\frac{\sqrt{1-k^{2}t^{2}}}{\sqrt{1-t^{2}}}\mathrm{d}t.}}
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