Multiple integral representations of the Catalan's constant
Number Theory
2026-05-12 v1
Abstract
In this paper, we present several novel integral representations of Catalan's constant. We begin by deriving an initial result expressed as a double integral. Subsequently, as a consequence of this result, we establish a general theorem that enables the representation of Catalan's constant in terms of a single integral. Finally, we provide a multiple integral representation of Catalan's constant in dimensions greater than or equal to two using the Lerch function. The results are accompanied by illustrative examples.
Cite
@article{arxiv.2605.08899,
title = {Multiple integral representations of the Catalan's constant},
author = {Emilio Gómez-Déniz and José María Sarabia},
journal= {arXiv preprint arXiv:2605.08899},
year = {2026}
}
Comments
10 pages