DLMF:19.4.E5 (Q6125): Difference between revisions

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DLMF:19.4.E5
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    F ( ϕ , k ) k = E ( ϕ , k ) - k 2 F ( ϕ , k ) k k 2 - k sin ϕ cos ϕ k 2 1 - k 2 sin 2 ϕ , partial-derivative elliptic-integral-first-kind-F italic-ϕ 𝑘 𝑘 elliptic-integral-second-kind-E italic-ϕ 𝑘 superscript superscript 𝑘 2 elliptic-integral-first-kind-F italic-ϕ 𝑘 𝑘 superscript superscript 𝑘 2 𝑘 italic-ϕ italic-ϕ superscript superscript 𝑘 2 1 superscript 𝑘 2 2 italic-ϕ {\displaystyle{\displaystyle\frac{\partial F\left(\phi,k\right)}{\partial k}={% \frac{E\left(\phi,k\right)-{k^{\prime}}^{2}F\left(\phi,k\right)}{k{k^{\prime}}% ^{2}}-\frac{k\sin\phi\cos\phi}{{k^{\prime}}^{2}\sqrt{1-k^{2}{\sin^{2}}\phi}}},}}
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    DLMF:19.4.E5
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