Some new and explicit identities related with the Appell-type degenerate q-Changhee polynomials

Feng Qi,Hyuck-In Kwon,Lee-Chae Jang

doi:10.1186/s13662-016-0912-5

Abstract

Recently, Kim, Kwon, and Seo (J. Nonlinear Sci. Appl. 9:2380-2392, 2016) studied the degenerate q-Changhee polynomials and numbers. In this paper, we consider the Appell-type degenerate q-Changhee polynomials and give some new and explicit identities related to these polynomials

Highlights

Let p be a fixed odd prime number
We denote the ring of p-adic integers and the field of p-adic numbers by Zp and Qp, respectively
For each f ∈ UD(Zp), the p-adic q-Volkenborn integral on Zp is defined by Kim to be

Summary

We recall that

UD(Zp) is the set of uniformly differentiable functions on Zp. For each f ∈ UD(Zp), the p-adic q-Volkenborn integral on Zp is defined by Kim to be. Kwon-Kim-Seo [ ] derived some identities of the degenerate Changhee polynomials which are given by the generating function λ λ + log( + λt). We recall that the gamma and beta functions are defined by the following definite integrals: for α > , β > ,. Kim, Kwon, and Seo [ ] defined the degenerate q-Changhee polynomials, a q-extension of We note that if x = , Chn,λ,q = Chn,λ,q( ) are called the degenerate q-Changhee numbers. If x = , Chn,λ,q = Chn,λ,q( ) are called the Appell-type degenerate q-Changhee numbers.

Continuing this process consecutively yields

Conclusions