English

Evaluation of multivariate integrals based on a duality identity for the Stieltjes transform

Number Theory 2022-10-27 v6

Abstract

A detailed study of a double integral representation of the Catalan's constant allows us to identify a duality identity for the Stieltjes transform on which it is based. This duality identity is then extended to an arbitrary dimensional integral and several special cases are deduced. On the way, we also highlight a relationship with some multivariate generalizations of the Riemann zeta function.

Keywords

Cite

@article{arxiv.2105.11771,
  title  = {Evaluation of multivariate integrals based on a duality identity for the Stieltjes transform},
  author = {Sarth Chavan and Christophe Vignat},
  journal= {arXiv preprint arXiv:2105.11771},
  year   = {2022}
}

Comments

26 pages

R2 v1 2026-06-24T02:26:19.402Z