Integrals Associated with the Digamma Integral Representation
General Mathematics
2023-08-29 v1
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.
Cite
@article{arxiv.2308.14154,
title = {Integrals Associated with the Digamma Integral Representation},
author = {Richard J. Mathar},
journal= {arXiv preprint arXiv:2308.14154},
year = {2023}
}
Comments
12 pages, no figures, C-source code in anc directory