Abstract

The aim of the present paper is to deal with introducing a new family of Changhee polynomials which is called degenerate $q$-Changhee polynomials with weight $\alpha$ by using $p$-adic $q$-integral on $\mathbb Z_p$. From this definition, we obtain some new summation formulae and properties. We also introduce the degenerate $q$-Changhee polynomials of higher-order with weight $\alpha$ and obtain some new interesting results.

Keywords and Phrases

Degenerate $q$-Changhee polynomials and numbers with weight $\alpha$; higher-order degenerate $q$-Changhee polynomials and numbers with weight $\alpha$, Stirling numbers of the first and second kind.

A.M.S. subject classification

11B68, 11B83, 11S80.

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