DLMF:25.11.E22
(Q7696)
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English
DLMF:25.11.E22
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Statements
Defining formula
ζ
′
(
1
-
2
n
,
1
2
)
=
-
B
2
n
ln
2
n
⋅
4
n
-
(
2
2
n
-
1
-
1
)
ζ
′
(
1
-
2
n
)
2
2
n
-
1
,
diffop
Hurwitz-zeta
1
1
2
𝑛
1
2
Bernoulli-number-B
2
𝑛
2
⋅
𝑛
superscript
4
𝑛
superscript
2
2
𝑛
1
1
diffop
Riemann-zeta
1
1
2
𝑛
superscript
2
2
𝑛
1
{\displaystyle{\displaystyle\zeta'\left(1-2n,\tfrac{1}{2}\right)=-\frac{B_{2n}% \ln 2}{n\cdot 4^{n}}-\frac{(2^{2n-1}-1)\zeta'\left(1-2n\right)}{2^{2n-1}},}}
0 references
DLMF id
DLMF:25.11.E22
0 references
constraint
n
=
1
,
2
,
3
,
…
𝑛
1
2
3
…
{\displaystyle{\displaystyle n=1,2,3,\dots}}
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