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Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function

Authors :
Kim, Taekyun
Kim, Dae san
jang, Lee-Chae
Lee, Hyunseok
Kim, Hanyoung
Publication Year :
2021

Abstract

In a previous paper, Rahmani introduced a new family of p-Bernoulli numbers and polynomials by means of the Gauss hypergeometric function. Motivated by this paper and as a degenerate version of those numbers and polynomials, we introduce the generalized degenerate Bernoulli numbers and polynomials again by using the Gauss hypergeometric function. In addition, we introduce the degenerate type Eulerian numbers as a degenerate version of Eulerian numbers. For the generalized degenerate Bernoulli numbers, we express them in terms of the degenerate Stirling numbers of the second kind, of the degenerate type Eulerian numbers, of the degenerate $p$-Stirling numbers of the second kind and of an integral on the unit interval. As to the generalized degenerate Bernoulli polynomials, we represent them in terms of the degenerate Stirling polynomials of the second kind.<br />Comment: 11 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2101.01893
Document Type :
Working Paper