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DLMF:19.6#Ex28 - MaRDI portal

DLMF:19.6#Ex28 (Q6868)

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DLMF:19.6#Ex28
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    DLMF defining formula
    Π ⁡ ( ϕ , k 2 , k ) = 1 k ′ 2 ⁢ ( E ⁡ ( ϕ , k ) - k 2 Δ ⁢ sin ⁡ ϕ ⁢ cos ⁡ ϕ ) , elliptic-integral-third-kind-Pi italic-ϕ superscript 𝑘 2 𝑘 1 superscript superscript 𝑘 ′ 2 elliptic-integral-second-kind-E italic-ϕ 𝑘 superscript 𝑘 2 Δ italic-ϕ italic-ϕ {\displaystyle{\displaystyle\Pi\left(\phi,k^{2},k\right)=\frac{1}{{k^{\prime}}% ^{2}}\left(E\left(\phi,k\right)-\frac{k^{2}}{\Delta}\sin\phi\cos\phi\right),}}
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