Bose integral
= Bose integral
{c}
For $\operatorname{Re}s>1$, expansion of $(e^x-1)^{-1}$ as a <geometric series> and termwise integration give
$$
\int_0^\infty\frac{x^{s-1}}{e^x-1}\,dx
=\Gamma(s)\zeta(s).
$$
= Bose integral
{c}
For $\operatorname{Re}s>1$, expansion of $(e^x-1)^{-1}$ as a <geometric series> and termwise integration give
$$
\int_0^\infty\frac{x^{s-1}}{e^x-1}\,dx
=\Gamma(s)\zeta(s).
$$