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DLMF:24.4.E32
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Formula:8138
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MaRDI QID
Q8138
Label: DLMF:24.4.E32
Digital Library of Mathematical Functions ID
24.4.E32
B
2
n
(
1
6
)
=
B
2
n
(
5
6
)
=
1
2
(
1
-
2
1
-
2
n
)
(
1
-
3
1
-
2
n
)
B
2
n
,
Bernoulli-polynomial-B
2
𝑛
1
6
Bernoulli-polynomial-B
2
𝑛
5
6
1
2
1
superscript
2
1
2
𝑛
1
superscript
3
1
2
𝑛
Bernoulli-number-B
2
𝑛
{\displaystyle{\displaystyle B_{2n}\left(\tfrac{1}{6}\right)=B_{2n}\left(% \tfrac{5}{6}\right)=\tfrac{1}{2}(1-2^{1-2n})(1-3^{1-2n})B_{2n},}}
Constraint(s)
Symbols List
B
n
Bernoulli-number-B
𝑛
{\displaystyle{\displaystyle B_{\NVar{n}}}}
:
B
n
(
x
)
Bernoulli-polynomial-B
𝑛
𝑥
{\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
:
n
𝑛
{\displaystyle{\displaystyle n}}
: integer
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