DLMF:25.11.E36
(Q7710)
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No description defined
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English
DLMF:25.11.E36
No description defined
Statements
Defining formula
L
(
s
,
χ
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
=
k
-
s
∑
r
=
1
k
-
1
χ
(
r
)
ζ
(
s
,
r
k
)
,
Dirichlet-L
𝑠
𝜒
superscript
subscript
𝑛
1
𝜒
𝑛
superscript
𝑛
𝑠
superscript
𝑘
𝑠
superscript
subscript
𝑟
1
𝑘
1
𝜒
𝑟
Hurwitz-zeta
𝑠
𝑟
𝑘
{\displaystyle{\displaystyle L\left(s,\chi\right)=\sum_{n=1}^{\infty}\frac{% \chi(n)}{n^{s}}=k^{-s}\sum_{r=1}^{k-1}\chi(r)\zeta\left(s,\frac{r}{k}\right),}}
0 references
DLMF id
DLMF:25.11.E36
0 references
constraint
ℜ
s
>
1
𝑠
1
{\displaystyle{\displaystyle\Re s>1}}
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