# Thread: Poles of an exponential function

1. ## Poles of an exponential function

This is a bit embarrassing since I know I've done this problem before.

I was trying to respond to a post and this problem came up. Where are the poles in the expression $\displaystyle e^{-z^2}= cos(z^2) - i ~ sin(z^2)$? I know it's a simple problem but I just can't wrap my mind about it.

Thanks!

-Dan

2. ## Re: Poles of an exponential function

Originally Posted by topsquark
Where are the poles in the expression $\displaystyle e^{-z^2}= cos(z^2) - i ~ sin(z^2)$? I know it's a simple problem but I just can't wrap my mind about it.
There are no poles, $\displaystyle f(z)=e^{-z^2}$ is holomorphic in $\displaystyle \mathbb{C}$.

3. ## Re: Poles of an exponential function

Originally Posted by FernandoRevilla
There are no poles, $\displaystyle f(z)=e^{-z^2}$ is holomorphic in $\displaystyle \mathbb{C}$.
Thanks. That was my first thought but I managed to make things complicated. It drives my students nuts because I will do a derivation in 10 lines that can often be done in two.

-Dan