Some identities on degenerate hyperbolic functions arising from $ p $-adic integrals on $ \mathbb{Z}_p $

Taekyun Kim; Hye Kyung Kim; Dae San Kim; Taekyun Kim; Hye Kyung Kim; Dae San Kim

doi:10.3934/math.20231298

AIMS Mathematics

2023, Volume 8, Issue 11: 25443-25453. doi: 10.3934/math.20231298

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Some identities on degenerate hyperbolic functions arising from $ p $-adic integrals on $ \mathbb{Z}_p $

1.
Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
2.
Department of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Republic of Korea
3.
Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea

Received: 02 July 2023 Revised: 07 August 2023 Accepted: 22 August 2023 Published: 31 August 2023
MSC : 11S80, 11B68, 11B83

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.
- Volkenborn integral,
- fermionic $ p $-adic integral,
- degenerate hyperbolic functions,
- degenerate Bernoulli numbers,
- degenerate Euler numbers,
- Cauchy numbers of the first kind
Citation: Taekyun Kim, Hye Kyung Kim, Dae San Kim. Some identities on degenerate hyperbolic functions arising from $ p $-adic integrals on $ \mathbb{Z}_p $[J]. AIMS Mathematics, 2023, 8(11): 25443-25453. doi: 10.3934/math.20231298

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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.

References

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