DLMF:5.7.E3 (Q2079)

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DLMF:5.7.E3
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    Statements

    test
    ln ⁡ Γ ⁡ ( 1 + z ) = - ln ⁡ ( 1 + z ) + z ⁢ ( 1 - γ ) + ∑ k = 2 ∞ ( - 1 ) k ⁢ ( ζ ⁡ ( k ) - 1 ) ⁢ z k k , Euler-Gamma 1 𝑧 1 𝑧 𝑧 1 superscript subscript 𝑘 2 superscript 1 𝑘 Riemann-zeta 𝑘 1 superscript 𝑧 𝑘 𝑘 {\displaystyle{\displaystyle\ln\Gamma\left(1+z\right)=-\ln\left(1+z\right)+z(1% -\gamma)+\sum_{k=2}^{\infty}(-1)^{k}(\zeta\left(k\right)-1)\frac{z^{k}}{k},}}
    0 references
    DLMF id
    DLMF:5.7.E3
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    constraint
    | z | < 2 𝑧 2 {\displaystyle{\displaystyle|z|<2}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
     
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