Riemann zeta as integral of monomial divided by an exponential

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Theorem

The following formula holds for $\rm{Re}(z)>1$: $$\zeta(z) = \dfrac{1}{\Gamma(z)} \displaystyle\int_0^{\infty} \dfrac{t^{z-1}}{e^t-1} \rm{d}t,$$ where $\zeta$ denotes the Riemann zeta function and $e^t$ denotes the exponential.

Proof

Videos

Zeta Integral by ei pi (5 July 2016)

References