Abstract

In this paper, we study $q$-analogue of Catalan numbers and polynomials by using $p$-adic $q$-integral on $\mathbb Z_p$. We investigate some properties of these numbers and polynomials. In addition, we define $q$-analogue of $\frac{1}{2}$-Changhee numbers by using $p$-adic $q$-integral on $\mathbb Z_p$ and derive their explicit expressions and some identities involving them.

Keywords and Phrases

Catalan numbers, $\frac{1}{2}$-Changhee numbers, $q$-Catalan numbers, $q$-analogue of $\frac{1}{2}$-Changhee numbers, $q$-Euler numbers.

A.M.S. subject classification

11B68, 11S40, 11S80.

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