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DLMF:25.6.E10
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Formula:8340
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MaRDI QID
Q8340
Label: DLMF:25.6.E10
Digital Library of Mathematical Functions ID
25.6.E10
ζ
(
4
)
=
36
17
∑
k
=
1
∞
1
k
4
(
2
k
k
)
.
Riemann-zeta
4
36
17
superscript
subscript
𝑘
1
1
superscript
𝑘
4
binomial
2
𝑘
𝑘
{\displaystyle{\displaystyle\zeta\left(4\right)=\frac{36}{17}\sum_{k=1}^{% \infty}\frac{1}{k^{4}\genfrac{(}{)}{0.0pt}{}{2k}{k}}.}}
Constraint(s)
Symbols List
ζ
(
s
)
Riemann-zeta
𝑠
{\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
: Riemann zeta function
(
m
n
)
binomial
𝑚
𝑛
{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
:
k
𝑘
{\displaystyle{\displaystyle k}}
: nonnegative integer
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