DLMF:19.6#Ex9 (Q6151)

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DLMF:19.6#Ex9
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    Statements

    Defining formula
    Π ⁡ ( α 2 , k ) → K ⁡ ( k ) - ( E ⁡ ( k ) / k ′ 2 ) , → complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 complete-elliptic-integral-first-kind-K 𝑘 complete-elliptic-integral-second-kind-E 𝑘 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)\to K\left(k\right)-% \left(E\left(k\right)/{k^{\prime}}^{2}\right),}}
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    DLMF id
    DLMF:19.6#Ex9
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    constraint
    α 2 → 1 + → superscript 𝛼 2 limit-from 1 {\displaystyle{\displaystyle\alpha^{2}\to 1+}}
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