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The residue of an analytic function f at a singularity a ∈ ℂ is the uniquely determined complex number c, such that the function

[tex]f(z) - \frac{c}{z-a}[/tex]

admits a primitive in a punctured neighborhood of the point a. (end statement)

I know I'm allowed to assume that f is analytic with a singularity at a, but beyond that I just can't tell if it's a biconditional I have to prove, or if it's just a conditional and if so which way. Thanks