# I tried identifying the residue

1. Jun 3, 2012

### hedipaldi

1. The problem statement, all variables and given/known data

how to compute the residue of 1/(cosh(z)^n) at z=ipi/2?

2. Relevant equations

b]3. The attempt at a solution[/b]
i tried to use cosh(z)=-isinh(z-ipi/2) and taylor expantion of this.then from expantion of 1/(1+z) and some algebraic manipulations i tried identifying the residue.it didn't realy worked

2. Jun 3, 2012

### scurty

Re: residues

Sometimes it is helpful to go to the Laurent series to find the coefficient of the $c_{-1}$ term. In this case it is easier to find the order of the zero in the denominator by taking derivatives. Since there are no roots in the numerator, the order of the zero is the order of the pole.