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arXiv · 2308.14154

Integrals Associated with the Digamma Integral Representation

Richard J. Mathar
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Abstract

The definite integral with the kernel x/(x^2+b^2)/[\exp(2\pi x)-1] integrated from x=0 to infinity is the main term of a representation of the Digamma-Function psi(b), the derivative of the logarithm of the Gamma-Function. We present relations within the set of integrals over x^n/(x^2+b^2)^j/[\exp(\mu x)-1]^s for small integer exponents n, j and s with the aim to reduce them all to Polygamma-Functions.

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Richard J. Mathar. 2023-08-27. Integrals Associated with the Digamma Integral Representation. https://arxiv.org/abs/2308.14154

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