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 $\mathbb Z_p$.

Keywords and Phrases

Degenerate Catalan numbers, $q$-analogue of degenerate $\frac{1}{2}$-Changhee numbers, $p$-adic $q$-integral on $\mathbb Z_p$.

A.M.S. subject classification

11B83, 11B73, 05A19.

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