Hurwitz Zeta Function - Hurwitz's Formula

Hurwitz's Formula

Hurwitz's formula is the theorem that

where

$\beta(x;s)= 2\Gamma(s+1)\sum_{n=1}^\infty \frac {\exp(2\pi inx) } {(2\pi n)^s}= \frac{2\Gamma(s+1)}{(2\pi)^s} \mbox{Li}_s (e^{2\pi ix})$

is a representation of the zeta that is valid for and s > 1. Here, is the polylogarithm.

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