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Gamma function

{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

Bernoulli formula for zeta values at nonpositive integers

Past exam of the mathematics course of the University of Cambridge / 2009 / ii / Paper 3 / 35D / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 137 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 35A / b / iv / Solution

Bose integral

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Bose integral

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