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.

Read more about this topic:  Hurwitz Zeta Function

Famous quotes containing the word formula:

    Ideals possess the strange quality that if they were completely realized they would turn into nonsense. One could easily follow a commandment such as “Thou shalt not kill” to the point of dying of starvation; and I might establish the formula that for the proper functioning of the mesh of our ideals, as in the case of a strainer, the holes are just as important as the mesh.
    Robert Musil (1880–1942)