# A problem of infinite series

1. Apr 9, 2007

### HolyPhia

1. The problem statement, all variables and given/known data
I don't know if there is an analytic expression of this infinite series:
$$f(x,y)=\sum_{n=0}^{+\infty}\frac{x^n}{1-y^n}$$
here $$x,y<1$$

2. Relevant equations
This series is convergent, so maybe it can be expressed as some special function?

3. The attempt at a solution
I tried to differentiate $$f(x,y)$$ with respect to x and y, to find some relationship between $$\frac{\partial f(x,y)}{\partial x}$$and $$\frac{\partial f(x,y)}{\partial y}$$,etc. But it seems no help...

Last edited: Apr 9, 2007