3
$\begingroup$

Consider the holomorphic function $f(z)=\sum\limits_{n=1}^{\infty}\frac{z^n}{n^2}$. How do I find the largest open set to which $f$ can be analytically continued? Is there a closed formula for $f$?

  • 0
    It can't be expressed elementarily. $-\int_0^z \frac{\log(1-t)}{t}\mathrm dt$ is what's termed as a *dilogarithm*...2011-10-04

1 Answers 1