Find the residue of the following.
(a) , where
(b) , where
We are just beginning residues right now, and I do not know how to proceed. Should I use the Laurent expansion to find the residue for both parts? I am not very familiar with residues yet. Thanks very much.
You have a Taylor series multiplied by a non-terminating singular series so the residue is an infinite sum due to the term-wise multiplication of by so then:
and note the coefficients on the terms are when the exponent of z is . Now, can you extract out all those terms and come up with the expression: