Riemann zeta as integral of monomial divided by an exponential

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.

References

• 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction $(3)$