# How to find laurent series of $\exp(1/z)$

I want to find the laurent series of $f(z)=\exp(1/z)$.

I started with the formula for laurent series: $f(z)=\sum_{0}^{\infty} a_n (z-z_0)^n +\sum_{1}^{\infty} b_n (z-z_0)^{-n}$, but I don't know how to apply it.

Can someone help me find the series?

• Do you know the series expansion for $f(w)=e^w$? If you do, write that out and then see what happens when $w=1/z$. – James Cameron Oct 19 '13 at 18:28
• @JamesCameron Yes that's it, thanks – Willy Oct 19 '13 at 18:42

## 1 Answer

(Posting a comment as an answer)

Do you know the series expansion for $f(w)=e^w$? If you do, write that out and then see what happens when $w=1/z$.