Study on q-analogues of Catala-Daehee numbers and polynomials

TL;DR

This paper introduces q-analogues of Catalan-Daehee numbers and polynomials using p-adic q-integrals, providing explicit formulas and extending the classical theory of these special numbers.

Contribution

It presents the first construction of q-analogues of Catalan-Daehee numbers and polynomials via p-adic q-integrals, with explicit expressions derived.

Findings

Explicit formulas for q-analogues derived

Extension of classical Catalan-Daehee numbers to q-analogues

New integral representations using p-adic q-integrals

Abstract

Catalan-Daehee numbers and polynomials, generating functions of which can be expressed as p-adic Volkenborn integrals on Zp, were studied previously. The aim of this paper is to introduce q-analogues of the catalan-Daehee numbers and polynomials with the help of p-adic q-integrals von Zp. We derive, among other thing, some explicit expressions for the q-analogues of the Catalan-Daehee numbers and polynomials.