AIMS Mathematics (Aug 2023)

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

  • Taekyun Kim,
  • Hye Kyung Kim ,
  • Dae San Kim

DOI
https://doi.org/10.3934/math.20231298
Journal volume & issue
Vol. 8, no. 11
pp. 25443 – 25453

Abstract

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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