# Elliptic functions, residue computation, same zeros and poles

1. Apr 1, 2017

### binbagsss

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

Hi,

I am trying to understand the attached:

I know that if two functions have zeros and poles at the same point and of the same order then they differ only by a multiplicative constant, so that is fine, as both have a double zero at $z=w_j/2$ and a double pole at $z=0$.

But I don't understand at all the idea before determining what the constant $C$ should be?
I thought that perhaps we had set the residues at the double pole $z=0$ equal, but this is given by:

$\frac{1}{2}lim_{z \to 0} \frac{d}{dz}(z^2f(z))$,

whereas it looks like we've compared

$lim_{z \to 0} z^{2} f(z)$,

so unless we have some reason to take the derivative outside the limit or something, I don't understand what we've done, and even whether my thoughts are on the right track and the residues are being compared?

2. Relevant equations

see above

3. The attempt at a solution

see above

2. Apr 6, 2017

bump