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 of special functions. It looks tantalizingly like the polylogarithm function. I tried using integral representations of the binomial coefficient, but to no avail. Any help is highly appreciated.
2026-03-26 19:37:45.1774553865
Evaluating a variant of the polylogarithm
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