DLMF:25.8.E2 (Q7659)

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DLMF:25.8.E2
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    Statements

    test
    ∑ k = 0 ∞ Γ ⁡ ( s + k ) ( k + 1 ) ! ⁢ ( ζ ⁡ ( s + k ) - 1 ) = Γ ⁡ ( s - 1 ) , superscript subscript 𝑘 0 Euler-Gamma 𝑠 𝑘 𝑘 1 Riemann-zeta 𝑠 𝑘 1 Euler-Gamma 𝑠 1 {\displaystyle{\displaystyle\sum_{k=0}^{\infty}\frac{\Gamma\left(s+k\right)}{(% k+1)!}\left(\zeta\left(s+k\right)-1\right)=\Gamma\left(s-1\right),}}
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    DLMF id
    DLMF:25.8.E2
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    constraint
    s ≠ 1 , 0 , - 1 , - 2 , … 𝑠 1 0 1 2 … {\displaystyle{\displaystyle s\neq 1,0,-1,-2,\dots}}
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