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DLMF:19.7#Ex13 - MaRDI portal

DLMF:19.7#Ex13 (Q6890)

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DLMF:19.7#Ex13
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    DLMF defining formula
    E ⁡ ( ϕ , i ⁢ k ) = ( 1 / κ ′ ) ⁢ ( E ⁡ ( θ , κ ) - κ 2 ⁢ ( sin ⁡ θ ⁢ cos ⁡ θ ) ⁢ ( 1 - κ 2 ⁢ sin 2 ⁡ θ ) - 1 / 2 ) , elliptic-integral-second-kind-E italic-ϕ 𝑖 𝑘 1 superscript 𝜅 ′ elliptic-integral-second-kind-E 𝜃 𝜅 superscript 𝜅 2 𝜃 𝜃 superscript 1 superscript 𝜅 2 2 𝜃 1 2 {\displaystyle{\displaystyle E\left(\phi,ik\right)=(1/\kappa^{\prime})\left(E% \left(\theta,\kappa\right)-\kappa^{2}\*(\sin\theta\cos\theta)\*(1-\kappa^{2}{% \sin^{2}}\theta)^{-\ifrac{1}{2}}\right),}}
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