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Definition: The constant a_(-1) in the Laurent series f(z) = sum_(n=-infinity)^infinity [a_n(z-z_0)^n] of f(z) about a point z_0 is called the residue of f(z). If f is analytic at z_0, its residue is zero, but the converse is not always true (for example, 1/z^2 has residue of 0 at z=0 but is not analytic at z=0).