Bose integral

For

Re s > 1

, expansion of

(e^{x} - 1)^{- 1}

as a geometric series and termwise integration give

\int_{0}^{\infty} \frac{x ^{s - 1}}{e ^{x} - 1} d x = Γ (s) ζ (s) .

 Ancestors (6)