DLMF:1.8.E12
(Q266)
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English
DLMF:1.8.E12
No description defined
Statements
Defining formula
∫
0
x
(
f
(
t
)
-
1
2
a
0
)
d
t
=
∑
n
=
1
∞
a
n
sin
(
n
x
)
+
b
n
(
1
-
cos
(
n
x
)
)
n
,
subscript
superscript
𝑥
0
𝑓
𝑡
1
2
subscript
𝑎
0
𝑡
subscript
superscript
𝑛
1
subscript
𝑎
𝑛
𝑛
𝑥
subscript
𝑏
𝑛
1
𝑛
𝑥
𝑛
{\displaystyle{\displaystyle\int^{x}_{0}(f(t)-\tfrac{1}{2}a_{0})\mathrm{d}t=% \sum^{\infty}_{n=1}\frac{a_{n}\sin\left(nx\right)+b_{n}(1-\cos\left(nx\right))% }{n},}}
0 references
DLMF id
DLMF:1.8.E12
0 references
constraint
0
≤
x
≤
2
π
0
𝑥
2
𝜋
{\displaystyle{\displaystyle 0\leq x\leq 2\pi}}
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