$\mathbb上$p$-dic积分引起的退化双曲函数的一些恒等式{Z}_p$

IF 1.8 3区数学 Q1 MATHEMATICS

AIMS Mathematics Pub Date : 2023-03-04 DOI:10.3934/math.20231298

Taekyun Kim, Dae San Kim, H. Kim

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引用次数: 0

摘要

本文的目的是引入几个退化双曲函数作为双曲函数的退化形式，评估退化双曲余弦和退化双曲正弦函数的Volkenborn积分和Fermion$p$-dic积分，并从中导出一些涉及退化伯努利数的恒等式，退化欧拉数和第一类柯西数。

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

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.

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来源期刊

AIMS Mathematics Mathematics-General Mathematics

CiteScore

3.40

自引率

13.60%

发文量

769

审稿时长

90 days

期刊介绍： AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.