Help me parse the logic of this statement

  1. So I have this statement that I'm supposed to prove and I cannot for the life of me figure out what parts I'm allowed to assume and what part I am expected to prove, here it is:


    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
     
  2. jcsd
  3. AlephZero

    AlephZero 7,298
    Science Advisor
    Homework Helper

    I think if means prove two things.

    1. The residue is a uniquely determined complex number c.
    2. f(x) has the property stated.
     
  4. Thanks for your input Aleph, but it's not the answer I want to hear lol. Can I get a second opinion?
     
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