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Mathematics
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Complex Analysis
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Residue Theorem
Residue Theorem
📜
The statement of the theorem
For a meromorphic function
f
f
f
inside and on a closed contour
γ
\gamma
γ
,
∮
γ
f
(
z
)
d
z
=
2
π
i
∑
k
Res
(
f
,
a
k
)
\oint_\gamma f(z) dz = 2\pi i \sum_{k} \text{Res}(f, a_k)
∮
γ
f
(
z
)
d
z
=
2
πi
∑
k
Res
(
f
,
a
k
)
, where the sum is over the singularities
a
k
a_k
a
k
inside
γ
\gamma
γ
.
Source: Wikipedia