On the Degenerate $(h,q)$-Changhee Numbers and Polynomials

Abstract

In this paper, we investigate a new $q$-analogue of the higher order degenerate Changhee polynomials and numbers, which are called the Witt-type formula for the $q$-analogue of degenerate Changhee polynomials of order $r$. We can derive some new interesting identities related to the degenerate $(h,q)$-Changhee polynomials and numbers.

Unified Degenerate Central Bell Polynomials

“…Kim et al [17] de…ned and studied on the extended degenerate r-central factorial numbers of the second kind and the extended degenerate rcentral Bell polynomials. Kwon et al [18] considered degenerate Changhee polynomials and proved several relations and formulas for these polynomials. Lim [19] de…ned higher order degenerate Genocchi polynomials and gave some identities and formulas for these polynomials.…”

A Note on Modified Degenerate Gamma and Laplace Transformation

“…At first, L. Carlitz introduced the degenerate special polynomials (see [1,2]). The recently works which can be cited in this and researchers have studied the degenerate special polynomials and numbers (see [4,[6][7][8][9][10][11][12][13]16,17]). Recently, the concept of degenerate gamma function and degenerate Laplace transform was introduced by Kim-Kim(2017).…”

A Note on Modified Degenerate Gamma and Laplace Transformation

“…At first, L. Carlitz introduced the degenerate special polynomials (see [6,7]). The recently works which can be cited in this and researchers have studied the degenerate special polynomials and numbers (see [2,[8][9][10][11][12][13][14][15][16][17][18][19]). Recently, the concept of degenerate gamma function and degenerate Laplace transformation was introduced by Kim-Kim [2].…”