March 3, 2026

New representations of Catalan’s constant obtained from the half hyperbolic secant distribution

Key Points

New representations of Catalan's constant were derived from the half hyperbolic secant distribution, indicating potential applications in mathematical analysis.
Significant findings include integral and series representations that improve the understanding of Catalan's constant.
Assessment using multi-faceted approaches like Lorenz curves and Gini indices led to these new expressions.
Highlights the importance of integrating various mathematical distributions to explore constants like Catalan's.

Abstract

Abstract Derived from the half hyperbolic secant distribution, new expressions and bounds for Catalan’s constant are presented. They are obtained by using expressions for the Lorenz curve, the Gini and Theil indices, convolutions, and a mixture of distributions, among other approaches. The new expressions are presented both in terms of integral (simple and double) representation and also as an interesting series representation. In addition, some integral representations of Apéry’s constant and Euler numbers are obtained.

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Cite This Study

Gómez-Déniz et al. (Wed,) studied this question.

synapsesocial.com/papers/69a75cbec6e9836116a25e0b https://doi.org/https://doi.org/10.1515/ms-2025-1150

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