Article overview
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.
AMS Subject Classification
11B68, 11S40, 11S80.
Reference information
How to Cite
Waseem Ahmad Khan, Vijay Yadav (2023). A NOTE ON $q$-ANALOGUE OF CATALAN NUMBERS ASSOCIATED WITH $q$-CHANGHEE NUMBERS. South East Asian Journal of Mathematics and Mathematical Sciences, 19(1), 29-42.