DLMF:25.8.E3 (Q7660)

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DLMF:25.8.E3
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    Statements

    Defining formula
    ∑ k = 0 ∞ ( s ) k ⁢ ζ ⁡ ( s + k ) k ! ⁢ 2 s + k = ( 1 - 2 - s ) ⁢ ζ ⁡ ( s ) , superscript subscript 𝑘 0 Pochhammer 𝑠 𝑘 Riemann-zeta 𝑠 𝑘 𝑘 superscript 2 𝑠 𝑘 1 superscript 2 𝑠 Riemann-zeta 𝑠 {\displaystyle{\displaystyle\sum_{k=0}^{\infty}\frac{{\left(s\right)_{k}}\zeta% \left(s+k\right)}{k!2^{s+k}}=(1-2^{-s})\zeta\left(s\right),}}
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    DLMF id
    DLMF:25.8.E3
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    constraint
    s ≠ 1 𝑠 1 {\displaystyle{\displaystyle s\neq 1}}
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