DLMF:19.25.E3 (Q6507)

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DLMF:19.25.E3
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    Defining formula
    Π ⁡ ( α 2 , k ) = 1 2 ⁢ π ⁢ R - 1 2 ⁡ ( 1 2 , - 1 2 , 1 ; k ′ 2 , 1 , 1 - α 2 ) , complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 1 2 𝜋 Carlson-integral-R 1 2 1 2 1 2 1 superscript superscript 𝑘 ′ 2 1 1 superscript 𝛼 2 {\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)=\tfrac{1}{2}\pi R_{-% \frac{1}{2}}\left(\tfrac{1}{2},-\tfrac{1}{2},1;{k^{\prime}}^{2},1,1-\alpha^{2}% \right),}}
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    DLMF id
    DLMF:19.25.E3
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