Suppose a punctured disk D = {z : 0 < z  c < R} in the complex plane is given and f is a holomorphic function defined (at least) on D. The residue of f at c, written as Res(f, c), is then defined as the coefficient a_{1} of (zc)^{1} in the Laurent series expansion of f around c. This coefficient can often be computed by combining several known Taylor series; it is also possible to use the integral formula given in the Laurent series article:
where γ traces out a circle around c in a counter clockwise manner.
If the function f can be continued to a holomorphic function on the whole disk {z : z  c < R}, then Res(f, c) = 0. The converse is not generally true.
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