Re: calculating a residue

Quote:

Originally Posted by

**Random Variable** I want to calculate the residue of

at

.

is a pole of order 2 since

So the standard approach is

After differentiating and applying L'Hospital's rule once, the limit is still indeterminate and very messy. Is there a better approach than repeated applications of L'Hospitals rule?

Try expanding as a series around , namely you should have an easy time then, no? By the way I hope you know..bam!

Re: calculating a residue

Here's what I did. It probably could have been done in less steps.

I wrote the function as . Then I found the Taylor series of centered at , and used synthetic division to find the Laurent series for centered at . Next I found the Taylor series for and centered at , and again used synthetic division to find the Laurent series for centered at . Finally I multiplied the Laurent series of by the Laurent series for .

Re: calculating a residue