Difference between revisions of "Relationship between Hurwitz zeta and gamma function"

Theorem: The following formula holds: $$\Gamma(s)\zeta(s,a) = \displaystyle\int_0^{\infty} \dfrac{x^{s-1}e^{-ax}}{1-e^{-x}} dx,$$ where $\Gamma$ denotes the gamma function and $\zeta$ denotes the Hurwitz zeta function.