Some identities on degenerate hyperbolic functions arising from $p$-adic integrals on $\mathbb{Z}_p$
Number Theory
2023-03-07 v1
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 -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
Cite
@article{arxiv.2303.02295,
title = {Some identities on degenerate hyperbolic functions arising from $p$-adic integrals on $\mathbb{Z}_p$},
author = {Taekyun Kim and Dae San Kim and Hye Kyung Kim},
journal= {arXiv preprint arXiv:2303.02295},
year = {2023}
}