
#1
Mar1712, 11:17 AM

P: 294

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}{za}[/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
Mar1712, 11:42 AM

Engineering
Sci Advisor
HW Helper
Thanks
P: 6,344

I think if means prove two things.
1. The residue is a uniquely determined complex number c. 2. f(x) has the property stated. 



#3
Mar1712, 02:28 PM

P: 294

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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