DLMF:19.8#Ex11 (Q6224)

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DLMF:19.8#Ex11
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    Defining formula
    E ⁡ ( ϕ , k ) = 1 2 ⁢ ( 1 + k ′ ) ⁢ E ⁡ ( ϕ 1 , k 1 ) - k ′ ⁢ F ⁡ ( ϕ , k ) + 1 2 ⁢ ( 1 - k ′ ) ⁢ sin ⁡ ϕ 1 . elliptic-integral-second-kind-E italic-ϕ 𝑘 1 2 1 superscript 𝑘 ′ elliptic-integral-second-kind-E subscript italic-ϕ 1 subscript 𝑘 1 superscript 𝑘 ′ elliptic-integral-first-kind-F italic-ϕ 𝑘 1 2 1 superscript 𝑘 ′ subscript italic-ϕ 1 {\displaystyle{\displaystyle E\left(\phi,k\right)=\tfrac{1}{2}(1+k^{\prime})E% \left(\phi_{1},k_{1}\right)-k^{\prime}F\left(\phi,k\right)+\tfrac{1}{2}(1-k^{% \prime})\sin\phi_{1}.}}
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    DLMF id
    DLMF:19.8#Ex11
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