DLMF:25.8.E8 (Q7665)

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DLMF:25.8.E8
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    Statements

    Defining formula
    ∑ k = 1 ∞ ζ ⁡ ( 2 ⁢ k ) k ⁢ z 2 ⁢ k = ln ⁡ ( π ⁢ z sin ⁡ ( π ⁢ z ) ) , superscript subscript 𝑘 1 Riemann-zeta 2 𝑘 𝑘 superscript 𝑧 2 𝑘 𝜋 𝑧 𝜋 𝑧 {\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{\zeta\left(2k\right)}{k}z% ^{2k}=\ln\left(\frac{\pi z}{\sin\left(\pi z\right)}\right),}}
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    DLMF id
    DLMF:25.8.E8
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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