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Evaluating a variant of the polylogarithm
Consider the infinite sum :
$$\sum_{m=1}^{\infty}\binom{m}{my}\frac{z^{m}}{m^{s}}\;\;\;\;s\in\mathbb{C},\;\;\;\;|z|<\frac{1}{2},\;\;\;\;\;0<y<1$$
I want to evaluate this summation in terms ...
