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Research Note | Open Access

Several expressions for moments of sums of hyperbolic secant random variables

Taekyun Kim1( ), Dae San Kim2
Department of Mathematics, Kwangwoon University, Seoul 139701, Korea
Department of Mathematics, Sogang University, Seoul 121742, Korea
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Abstract

In this paper, we find several expressions for the moments of the hyperbolic secant distribution and the moments of the sum of two independent distributions. They are expressed in terms of Euler and Bernoulli numbers, zeta values, an integral representation, and certain infinite series.

Keywords

hyperbolic secant random variableEuler numbersBernoulli numbers

References

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Electronic Research Archive
Volume 33 Issue 9,
September 2025
Pages 5457-5470
DOI: 10.3934/era.2025244

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Cite this article:
Kim T, Kim DS. Several expressions for moments of sums of hyperbolic secant random variables. Electronic Research Archive, 2025, 33(9): 5457-5470. https://doi.org/10.3934/era.2025244

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Received: 08 July 2025
Revised: 18 August 2025
Accepted: 08 September 2025
Published: 15 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)