# An Exercise about Luarent Series

#### Gintoki

It's an exercise in Luarent Series.How to prove it?

f(Z)=1/z+$$\displaystyle sum_{n=1}^{infinity}a_{n}z^n$$ is univalent and holomorphic in domain B(0,1)\{1}. Prove that
$$\displaystyle sum_{n=1}^{infinity}n\left|a_{n}\right|^2$$ <=1

Is it called Area Theorem?

#### Bruno J.

MHF Hall of Honor
You probably mean $$\displaystyle B(0,1)-\{0\}$$ (the punctured unit disc)?

This is a fairly standard proof which can be found easily. Check back if you don't understand the proof!

#### Gintoki

I didn't find the proof actually. But the professor has gave the proof after I handed in my homework(Crying)

#### Bruno J.

MHF Hall of Honor