DLMF:19.8.E9 (Q6217)

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DLMF:19.8.E9
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    Statements

    Defining formula
    Π ⁡ ( α 2 , k ) = π 4 ⁢ M ⁡ ( 1 , k ′ ) ⁢ k 2 k 2 - α 2 ⁢ ∑ n = 0 ∞ Q n , complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 𝜋 4 arithmetic-geometric-mean 1 superscript 𝑘 ′ superscript 𝑘 2 superscript 𝑘 2 superscript 𝛼 2 superscript subscript 𝑛 0 subscript 𝑄 𝑛 {\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)=\frac{\pi}{4M\left(1,% k^{\prime}\right)}\frac{k^{2}}{k^{2}-\alpha^{2}}\sum_{n=0}^{\infty}Q_{n},}}
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    DLMF id
    DLMF:19.8.E9
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    constraint
    1 < α 2 < ∞ 1 superscript 𝛼 2 {\displaystyle{\displaystyle 1<\alpha^{2}<\infty}}
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