DLMF:25.8.E7 (Q7664)

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DLMF:25.8.E7
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    Statements

    Defining formula
    ∑ k = 2 ∞ ζ ⁡ ( k ) k ⁢ z k = - γ ⁢ z + ln ⁡ Γ ⁡ ( 1 - z ) , superscript subscript 𝑘 2 Riemann-zeta 𝑘 𝑘 superscript 𝑧 𝑘 𝑧 Euler-Gamma 1 𝑧 {\displaystyle{\displaystyle\sum_{k=2}^{\infty}\frac{\zeta\left(k\right)}{k}z^% {k}=-\gamma z+\ln\Gamma\left(1-z\right),}}
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    DLMF id
    DLMF:25.8.E7
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
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    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aadec
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