Multiple integral representations of the Catalan's constant

Emilio Gómez-Déniz; José María Sarabia

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arXiv · 2605.08899

Multiple integral representations of the Catalan's constant

Emilio Gómez-Déniz·José María Sarabia

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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.

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Emilio Gómez-Déniz, José María Sarabia. 2026-05-09. Multiple integral representations of the Catalan's constant. https://arxiv.org/abs/2605.08899

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