DLMF:5.7.E5 (Q2081)

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DLMF:5.7.E5
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    test
    ψ ⁡ ( 1 + z ) = 1 2 ⁢ z - π 2 ⁢ cot ⁡ ( π ⁢ z ) + 1 z 2 - 1 + 1 - γ - ∑ k = 1 ∞ ( ζ ⁡ ( 2 ⁢ k + 1 ) - 1 ) ⁢ z 2 ⁢ k , digamma 1 𝑧 1 2 𝑧 𝜋 2 𝜋 𝑧 1 superscript 𝑧 2 1 1 superscript subscript 𝑘 1 Riemann-zeta 2 𝑘 1 1 superscript 𝑧 2 𝑘 {\displaystyle{\displaystyle\psi\left(1+z\right)=\frac{1}{2z}-\frac{\pi}{2}% \cot\left(\pi z\right)+\frac{1}{z^{2}-1}+1-\gamma-\sum_{k=1}^{\infty}(\zeta% \left(2k+1\right)-1)z^{2k},}}
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    DLMF id
    DLMF:5.7.E5
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