Is there any closed form for the following series?

Question

I am looking for any closed form expression for the series given below: $$ \sum_{m \ge 1} \frac{(xy)^m}{m(1-y^m)}. $$

Answer 1

A closed for exists (attachment bellow) for the sum : $$ \sum_{m \ge 1} \frac{(xy)^m}{(1-y^m)} $$ thanks to the special function called q-digamma. See : http://mathworld.wolfram.com/q-PolygammaFunction.html

By integration, a closed form for the sum : $$ \sum_{m \ge 1} \frac{(xy)^m}{m(1-y^m)} $$ is formally expressed.

I cannot say if a simpler form can be derived.