DLMF:19.12.E4 (Q6302)

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DLMF:19.12.E4
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    Defining formula
    ( 1 - α 2 ) ⁢ Π ⁡ ( α 2 , k ) = ( ln ⁡ 4 k ′ ) ⁢ ( 1 + O ⁡ ( k ′ 2 ) ) - α 2 ⁢ R C ⁡ ( 1 , 1 - α 2 ) , 1 superscript 𝛼 2 complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 4 superscript 𝑘 ′ 1 Big-O superscript superscript 𝑘 ′ 2 superscript 𝛼 2 Carlson-integral-RC 1 1 superscript 𝛼 2 {\displaystyle{\displaystyle(1-\alpha^{2})\Pi\left(\alpha^{2},k\right)=\left(% \ln\frac{4}{k^{\prime}}\right)\left(1+O\left({k^{\prime}}^{2}\right)\right)-% \alpha^{2}R_{C}\left(1,1-\alpha^{2}\right),}}
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    DLMF id
    DLMF:19.12.E4
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