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Statements
(
-
1
)
k
ζ
(
k
)
(
-
2
n
)
=
2
(
-
1
)
n
(
2
π
)
2
n
+
1
∑
m
=
0
k
∑
r
=
0
m
(
k
m
)
(
m
r
)
ℑ
(
c
k
-
m
)
Γ
(
r
)
(
2
n
+
1
)
ζ
(
m
-
r
)
(
2
n
+
1
)
,
superscript
1
𝑘
Riemann-zeta
𝑘
2
𝑛
2
superscript
1
𝑛
superscript
2
𝜋
2
𝑛
1
superscript
subscript
𝑚
0
𝑘
superscript
subscript
𝑟
0
𝑚
binomial
𝑘
𝑚
binomial
𝑚
𝑟
superscript
𝑐
𝑘
𝑚
Euler-Gamma
𝑟
2
𝑛
1
Riemann-zeta
𝑚
𝑟
2
𝑛
1
{\displaystyle{\displaystyle(-1)^{k}{\zeta^{(k)}}\left(-2n\right)=\frac{2(-1)^%
{n}}{(2\pi)^{2n+1}}\sum_{m=0}^{k}\sum_{r=0}^{m}\genfrac{(}{)}{0.0pt}{}{k}{m}%
\genfrac{(}{)}{0.0pt}{}{m}{r}\Im(c^{k-m})\*{\Gamma^{(r)}}\left(2n+1\right){%
\zeta^{(m-r)}}\left(2n+1\right),}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
ζ
(
s
)
Riemann-zeta
𝑠
{\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
(
m
n
)
binomial
𝑚
𝑛
{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
π
{\displaystyle{\displaystyle\pi}}
ℑ
absent
{\displaystyle{\displaystyle\Im}}
k
𝑘
{\displaystyle{\displaystyle k}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
𝑛
{\displaystyle{\displaystyle n}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
