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Statements
ζ
(
m
+
s
)
=
(
-
1
)
m
-
1
Γ
(
s
)
sin
(
π
s
)
π
Γ
(
m
+
s
)
∫
0
∞
ψ
(
m
)
(
1
+
x
)
x
-
s
d
x
,
Riemann-zeta
𝑚
𝑠
superscript
1
𝑚
1
Euler-Gamma
𝑠
𝜋
𝑠
𝜋
Euler-Gamma
𝑚
𝑠
superscript
subscript
0
digamma
𝑚
1
𝑥
superscript
𝑥
𝑠
𝑥
{\displaystyle{\displaystyle\zeta\left(m+s\right)=(-1)^{m-1}\frac{\Gamma\left(%
s\right)\sin\left(\pi s\right)}{\pi\Gamma\left(m+s\right)}\*\int_{0}^{\infty}{%
\psi^{(m)}}\left(1+x\right)x^{-s}\mathrm{d}x,}}
m
=
1
,
2
,
3
,
…
𝑚
1
2
3
…
{\displaystyle{\displaystyle m=1,2,3,\dots}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
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}}}
ψ
(
z
)
digamma
𝑧
{\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
∫
{\displaystyle{\displaystyle\int}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
m
𝑚
{\displaystyle{\displaystyle m}}
x
𝑥
{\displaystyle{\displaystyle x}}
s
𝑠
{\displaystyle{\displaystyle s}}
Identifiers
