DLMF:19.8.E5 (Q6211)

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DLMF:19.8.E5
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    Statements

    Defining formula
    K ⁡ ( k ) = π 2 ⁢ M ⁡ ( 1 , k ′ ) , complete-elliptic-integral-first-kind-K 𝑘 𝜋 2 arithmetic-geometric-mean 1 superscript 𝑘 ′ {\displaystyle{\displaystyle K\left(k\right)=\frac{\pi}{2M\left(1,k^{\prime}% \right)},}}
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    DLMF id
    DLMF:19.8.E5
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    constraint
    - ∞ < k 2 < 1 superscript 𝑘 2 1 {\displaystyle{\displaystyle-\infty<k^{2}<1}}
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