Closed form of $\displaystyle\sum_{n=1}^\infty x^n\ln(n)$ Is there a closed form of this : 
$$\sum_{n=1}^\infty x^n\ln(n),$$
 where $|x|<1$.
Thanks in advance.

By definition, $\displaystyle\sum_{n=1}^\infty\frac{x^n}{n^a}=\text{Li}_a(x)$. Now, differentiate both sides with regard to a, and then let $a=0$.
