No.. Do you remember what residue is?
Hi
I was wondering whether someone would be able to have a look at this question and my answer to see if I am correct. If I am not, or the solution requires more information, I would greatly appreciate it if you could show me how solve this problem.
QUESTION:
Find Res(g,0) for g(z) = z^-2 . cosh(z) (I mean z squared multiplied by cosh(z))
MY SOLUTION
= cosh(z) / z^2
cosh(z) = 1 + z^2/2! + z^4/4! + z^6/6!
cosh(z)/z^2 = 1/z^2 + 1/2! + z^2/4! + z^4/6! + .....
This has a pole of order 2 at z = 0
Res(g,0) = 1/2
Thank you
Doug
See this post to see a derivation of Residue Theorem and why is called residue.
It's called residue because when you integrate the Laurent series of f(z), only the term is left.
Definition: Residue is the negative first terms coefficient.
Can you see any term in the form in your expansion?