Hey Folks, first post here,(adsbygoogle = window.adsbygoogle || []).push({});

I'm having significant difficulty understanding how to create an analytic continuation of a function. The topic seems straightforward (please stop me if I am wrong): if you have two functions whose laurent expansions have a radius of convergence > 0, then the functions must be equal on the domain where those radii of convergence overlap (this is likely a gross oversimplification as the topic was just introduced yesterday.)

My question is as to how you actually construct an analytic continuation of a function — say the log(z) function, with a branch cut taken from (-∞,0), to find an analytic continuation of the function on that branch cut minus the pole at z = 0.

Again this is still probably a gross oversimplification so I would really appreciate any advice/suggestions you guys have.

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# On Analytic Continuations of complex-valued functions

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