A STUDY ON $q$-ANALOGUE OF DEGENERATE $\frac{1}{2}$-CHANGHEE NUMBERS AND POLYNOMIALS

Abstract

The aim of the paper is to introduce $q$-analogue of degenerate $\frac{1}{2}$-Changhee numbers $Ch_{n,q,\lambda,\frac{1}{2}}$ with the help of a $p$-adic $q$-integral on $\mathbb Z_p$ and derive explicit expressions and some identities for those numbers. In more detail, we deduce explicit expressions of $Ch_{n,q,\lambda,\frac{1}{2}}$, as a rational function in terms of Euler number and Stirling numbers of the first kind, as a fermionic $p$-adic $q$-integral on $\mathbb Z_p$.