DLMF:19.8#Ex23 (Q6237)

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DLMF:19.8#Ex23
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    Defining formula
    E ⁡ ( ϕ , k ) = ( 1 + k ′ ) ⁢ E ⁡ ( ψ 1 , k 1 ) - k ′ ⁢ F ⁡ ( ϕ , k ) + ( 1 - Δ ) ⁢ cot ⁡ ϕ , elliptic-integral-second-kind-E italic-ϕ 𝑘 1 superscript 𝑘 ′ elliptic-integral-second-kind-E subscript 𝜓 1 subscript 𝑘 1 superscript 𝑘 ′ elliptic-integral-first-kind-F italic-ϕ 𝑘 1 Δ italic-ϕ {\displaystyle{\displaystyle E\left(\phi,k\right)=(1+k^{\prime})E\left(\psi_{1% },k_{1}\right)-k^{\prime}F\left(\phi,k\right)+(1-\Delta)\cot\phi,}}
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    DLMF id
    DLMF:19.8#Ex23
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