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Research Article | Open Access

Some identities on degenerate hyperbolic functions arising from p-adic integrals on Z p

Taekyun Kim1( ), Hye Kyung Kim2, Dae San Kim3
Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
Department of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Republic of Korea
Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
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Abstract

The aim of this paper is to introduce several degenerate hyperbolic functions as degenerate versions of the hyperbolic functions, to evaluate Volkenborn and the fermionic p-adic integrals of the degenerate hyperbolic cosine and the degenerate hyperbolic sine functions and to derive from them some identities involving the degenerate Bernoulli numbers, the degenerate Euler numbers and the Cauchy numbers of the first kind.

Keywords

Volkenborn integralfermionic p-adic integraldegenerate hyperbolic functionsdegenerate Bernoulli numbersdegenerate Euler numbersCauchy numbers of the first kind
CLC number: 11S80, 11B68, 11B83

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 25443-25453
DOI: 10.3934/math.20231298

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Cite this article:
Kim T, Kim HK, Kim DS. Some identities on degenerate hyperbolic functions arising from p-adic integrals on Z p . AIMS Mathematics, 2023, 8(11): 25443-25453. https://doi.org/10.3934/math.20231298

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Received: 02 July 2023
Revised: 07 August 2023
Accepted: 22 August 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

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