DLMF:19.6.E5 (Q6149)

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DLMF:19.6.E5
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    Statements

    Defining formula
    Π ⁡ ( α 2 , k ) = K ⁡ ( k ) - Π ⁡ ( k 2 / α 2 , k ) , complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 complete-elliptic-integral-first-kind-K 𝑘 complete-elliptic-integral-third-kind-Pi superscript 𝑘 2 superscript 𝛼 2 𝑘 {\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)=K\left(k\right)-\Pi% \left(k^{2}/\alpha^{2},k\right),}}
    0 references
    DLMF id
    DLMF:19.6.E5
    0 references
    Symbols used
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1acdec
    0 references
     
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