DLMF:19.7#Ex20 (Q6201)

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DLMF:19.7#Ex20
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    Defining formula
    E ⁡ ( i ⁢ ϕ , k ) = i ⁢ ( F ⁡ ( ψ , k ′ ) - E ⁡ ( ψ , k ′ ) + ( tan ⁡ ψ ) ⁢ 1 - k ′ 2 ⁢ sin 2 ⁡ ψ ) , elliptic-integral-second-kind-E 𝑖 italic-ϕ 𝑘 𝑖 elliptic-integral-first-kind-F 𝜓 superscript 𝑘 ′ elliptic-integral-second-kind-E 𝜓 superscript 𝑘 ′ 𝜓 1 superscript superscript 𝑘 ′ 2 2 𝜓 {\displaystyle{\displaystyle E\left(i\phi,k\right)=i\left(F\left(\psi,k^{% \prime}\right)-E\left(\psi,k^{\prime}\right)+(\tan\psi)\sqrt{1-{k^{\prime}}^{2% }{\sin^{2}}\psi}\right),}}
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    DLMF id
    DLMF:19.7#Ex20
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