logicalmoron
Oct22-09, 05:30 PM
Hey Folks, first post here,
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.
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.