DLMF:25.11.E38 (Q7712)

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DLMF:25.11.E38
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    Statements

    test
    ∑ k = 1 ∞ ( n + k k ) ⁢ ζ ⁡ ( n + k + 1 , a ) ⁢ z k = ( - 1 ) n n ! ⁢ ( ψ ( n ) ⁡ ( a ) - ψ ( n ) ⁡ ( a - z ) ) , superscript subscript 𝑘 1 binomial 𝑛 𝑘 𝑘 Hurwitz-zeta 𝑛 𝑘 1 𝑎 superscript 𝑧 𝑘 superscript 1 𝑛 𝑛 digamma 𝑛 𝑎 digamma 𝑛 𝑎 𝑧 {\displaystyle{\displaystyle\sum_{k=1}^{\infty}\genfrac{(}{)}{0.0pt}{}{n+k}{k}% \zeta\left(n+k+1,a\right)z^{k}=\frac{(-1)^{n}}{n!}\left({\psi^{(n)}}\left(a% \right)-{\psi^{(n)}}\left(a-z\right)\right),}}
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    DLMF id
    DLMF:25.11.E38
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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