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Statements
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,}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
γ
{\displaystyle{\displaystyle\gamma}}
ζ
(
s
)
Riemann-zeta
𝑠
{\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
Ln
z
multivalued-natural-logarithm
𝑧
{\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
s
𝑠
{\displaystyle{\displaystyle s}}
z
𝑧
{\displaystyle{\displaystyle z}}
