DLMF:5.9.E11 (Q2100)

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DLMF:5.9.E11
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    Defining formula
    Ln ⁡ Γ ⁡ ( z + 1 ) = - γ ⁢ z - 1 2 ⁢ π ⁢ i ⁢ ∫ - c - ∞ ⁢ i - c + ∞ ⁢ i π ⁢ z - s s ⁢ sin ⁡ ( π ⁢ s ) ⁢ ζ ⁡ ( - s ) ⁢ d s , multivalued-natural-logarithm Euler-Gamma 𝑧 1 𝑧 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 𝜋 superscript 𝑧 𝑠 𝑠 𝜋 𝑠 Riemann-zeta 𝑠 𝑠 {\displaystyle{\displaystyle\operatorname{Ln}\Gamma\left(z+1\right)=-\gamma z-% \frac{1}{2\pi i}\int_{-c-\infty i}^{-c+\infty i}\frac{\pi z^{-s}}{s\sin\left(% \pi s\right)}\zeta\left(-s\right)\mathrm{d}s,}}
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    DLMF id
    DLMF:5.9.E11
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