Poles of an exponential function

• Dec 2nd 2012, 09:18 AM
topsquark
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. (Headbang)

Thanks!

-Dan
• Dec 2nd 2012, 11:05 AM
FernandoRevilla
Re: Poles of an exponential function
Quote:

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}\$. :)
• Dec 2nd 2012, 12:08 PM
topsquark
Re: Poles of an exponential function
Quote:

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