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A problem of infinite series

  1. Apr 9, 2007 #1
    1. The problem statement, all variables and given/known data
    I don't know if there is an analytic expression of this infinite series:
    [tex]f(x,y)=\sum_{n=0}^{+\infty}\frac{x^n}{1-y^n}[/tex]
    here [tex]x,y<1[/tex]

    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 [tex]f(x,y)[/tex] with respect to x and y, to find some relationship between [tex]\frac{\partial f(x,y)}{\partial x}[/tex]and [tex]\frac{\partial f(x,y)}{\partial y}[/tex],etc. But it seems no help...
     
    Last edited: Apr 9, 2007
  2. jcsd
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