English

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.

Keywords

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

R2 v1 2026-07-01T12:59:52.637Z