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Statements
f
n
-
g
n
=
1
2
π
i
∫
|
z
|
=
r
f
(
z
)
-
g
(
z
)
z
n
+
1
d
z
=
1
2
π
r
n
∫
0
2
π
(
f
(
r
e
i
θ
)
-
g
(
r
e
i
θ
)
)
e
-
n
i
θ
d
θ
.
subscript
𝑓
𝑛
subscript
𝑔
𝑛
1
2
𝜋
𝑖
subscript
𝑧
𝑟
𝑓
𝑧
𝑔
𝑧
superscript
𝑧
𝑛
1
𝑧
1
2
𝜋
superscript
𝑟
𝑛
superscript
subscript
0
2
𝜋
𝑓
𝑟
superscript
𝑒
𝑖
𝜃
𝑔
𝑟
superscript
𝑒
𝑖
𝜃
superscript
𝑒
𝑛
𝑖
𝜃
𝜃
{\displaystyle{\displaystyle f_{n}-g_{n}=\frac{1}{2\pi i}\int_{|z|=r}\frac{f(z%
)-g(z)}{z^{n+1}}\mathrm{d}z=\frac{1}{2\pi r^{n}}\int_{0}^{2\pi}\left(f\left(re%
^{i\theta}\right)-g\left(re^{i\theta}\right)\right)e^{-ni\theta}\mathrm{d}%
\theta.}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
f
(
x
)
𝑓
𝑥
{\displaystyle{\displaystyle f(x)}}
f
n
subscript
𝑓
𝑛
{\displaystyle{\displaystyle f_{n}}}
r
𝑟
{\displaystyle{\displaystyle r}}
g
(
z
)
𝑔
𝑧
{\displaystyle{\displaystyle g(z)}}
g
n
subscript
𝑔
𝑛
{\displaystyle{\displaystyle g_{n}}}
Identifiers
