Degenerate, partially degenerate and totally degenerate Daehee numbers and polynomials

作者：Lim Dongkyu^*

来源：Advances in Difference Equations, 2015, 2015(1): 287.

DOI：10.1186/s13662-015-0624-2

• degenerate Daehee polynomial
• partially degenerate Daehee polynomial
• totally degenerate Daehee polynomial
• q-analogues of degenerate Daehee polynomial

Recently, Kim and Seo considered the partially degenerate Bernoulli numbers and polynomials of the first kind and of the second kind and investigated some properties of these numbers and polynomials. In this paper, we consider degenerate Daehee numbers and polynomials and extend them to partially and totally degenerate Daehee numbers and polynomials. We give some properties and identities and relate those numbers and polynomials with Daehee polynomials and Bernoulli polynomials of the second kind. Some q-analogues of the degenerate Bernoulli polynomials are studied by Kim et al. This research influenced us to study q-analogues of the degenerate Daehee numbers and polynomials. We also study q-analogues of partially and totally degenerate Daehee numbers and polynomials. And we give some formulas related to those numbers and polynomials.

• 出版日期2015-9-16