Generalized Stieltjes constants and integrals involving the log-log function: Kummer's Theorem in action
Classical Analysis and ODEs
2017-02-20 v1
Abstract
In this note, we recall Kummer's Fourier series expansion of the 1-periodic function that coincides with the logarithm of the Gamma function on the unit interval , and we use it to find closed forms for some numerical series related to the generalized Stieltjes constants, and some integrals involving the function .
Cite
@article{arxiv.1702.05439,
title = {Generalized Stieltjes constants and integrals involving the log-log function: Kummer's Theorem in action},
author = {Omran Kouba},
journal= {arXiv preprint arXiv:1702.05439},
year = {2017}
}