English

The Fourier series of the log-Barnes function

Classical Analysis and ODEs 2016-04-05 v1

Abstract

In this paper we determine the Fourier series expansion of the log-Barnes function. This is the analogue of the classical result of Kummer and Malmsten. Applying this expansion we get some integrals similar to the Espinosa-Moll log-Gamma integrals with respect to logG\log G. During the course of the paper some interesting log-Gamma integrals and a log-harmonic sum are evaluated.

Keywords

Cite

@article{arxiv.1604.00753,
  title  = {The Fourier series of the log-Barnes function},
  author = {István Mező},
  journal= {arXiv preprint arXiv:1604.00753},
  year   = {2016}
}