Poles of an exponential function

**topsquark** · December 2nd 2012, 09:18 AM

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 $e^{-z^2}= cos(z^2) - i ~ sin(z^2)$ ? I know it's a simple problem but I just can't wrap my mind about it.

Thanks!

-Dan

**FernandoRevilla** · December 2nd 2012, 11:05 AM

Originally Posted by topsquark

Where are the poles in the expression $e^{-z^2}= cos(z^2) - i ~ sin(z^2)$ ? I know it's a simple problem but I just can't wrap my mind about it.

There are no poles, $f(z)=e^{-z^2}$ is holomorphic in $\mathbb{C}$ .

**topsquark** · December 2nd 2012, 12:08 PM

Originally Posted by FernandoRevilla

There are no poles, $f(z)=e^{-z^2}$ is holomorphic in $\mathbb{C}$ .

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

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