DLMF:19.6#Ex5 (Q6145)

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DLMF:19.6#Ex5
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    Statements

    Defining formula
    Π ⁡ ( - k , k ) = 1 4 ⁢ π ⁢ ( 1 + k ) - 1 + 1 2 ⁢ K ⁡ ( k ) , complete-elliptic-integral-third-kind-Pi 𝑘 𝑘 1 4 𝜋 superscript 1 𝑘 1 1 2 complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle\Pi\left(-k,k\right)=\tfrac{1}{4}\pi(1+k)^{-1}+% \tfrac{1}{2}K\left(k\right),}}
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    DLMF id
    DLMF:19.6#Ex5
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    constraint
    0 ≤ k 2 < 1 0 superscript 𝑘 2 1 {\displaystyle{\displaystyle 0\leq k^{2}<1}}
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