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Statements
B
2
n
(
x
)
=
(
-
1
)
n
+
1
2
n
∫
0
∞
cos
(
2
π
x
)
-
e
-
2
π
t
cosh
(
2
π
t
)
-
cos
(
2
π
x
)
t
2
n
-
1
d
t
,
Bernoulli-polynomial-B
2
𝑛
𝑥
superscript
1
𝑛
1
2
𝑛
superscript
subscript
0
2
𝜋
𝑥
superscript
𝑒
2
𝜋
𝑡
2
𝜋
𝑡
2
𝜋
𝑥
superscript
𝑡
2
𝑛
1
𝑡
{\displaystyle{\displaystyle B_{2n}\left(x\right)=(-1)^{n+1}2n\*\int_{0}^{%
\infty}\frac{\cos\left(2\pi x\right)-e^{-2\pi t}}{\cosh\left(2\pi t\right)-%
\cos\left(2\pi x\right)}t^{2n-1}\mathrm{d}t,}}
n
=
1
,
2
,
…
𝑛
1
2
…
{\displaystyle{\displaystyle n=1,2,\dots}}
B
n
(
x
)
Bernoulli-polynomial-B
𝑛
𝑥
{\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
∫
{\displaystyle{\displaystyle\int}}
n
𝑛
{\displaystyle{\displaystyle n}}
t
𝑡
{\displaystyle{\displaystyle t}}
x
𝑥
{\displaystyle{\displaystyle x}}
