DLMF:19.7#Ex21 (Q6202)

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DLMF:19.7#Ex21
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    Defining formula
    Π ⁡ ( i ⁢ ϕ , α 2 , k ) = i ⁢ ( F ⁡ ( ψ , k ′ ) - α 2 ⁢ Π ⁡ ( ψ , 1 - α 2 , k ′ ) ) / ( 1 - α 2 ) . elliptic-integral-third-kind-Pi 𝑖 italic-ϕ superscript 𝛼 2 𝑘 𝑖 elliptic-integral-first-kind-F 𝜓 superscript 𝑘 ′ superscript 𝛼 2 elliptic-integral-third-kind-Pi 𝜓 1 superscript 𝛼 2 superscript 𝑘 ′ 1 superscript 𝛼 2 {\displaystyle{\displaystyle\Pi\left(i\phi,\alpha^{2},k\right)=i\left(F\left(% \psi,k^{\prime}\right)-\alpha^{2}\Pi\left(\psi,1-\alpha^{2},k^{\prime}\right)% \right)/{(1-\alpha^{2})}.}}
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    DLMF id
    DLMF:19.7#Ex21
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