A Note on q-analogue of Degenerate Catalan Numbers Associated with p-adic Integral on Zp

Abstract

In this paper, we introduce q-analogues of degenerate Catalan numbers and polynomials with the help of a fermionic p-adic q-integrals on Zp and establish some new connections with the degenerate Stirling numbers of the first and second kinds. Furthermore, we also find a few new identities and results of this type of polynomials and numbers.

A Note on Degenerate Catalan-Daehee Numbers and Polynomials

“…Upon setting ξ = 0 in (25), we have d m,λ (0) := d m,λ called the degenerate Catalan-Daehee numbers in (15). Theorem 8.…”

“…[1][2][3][4]8,10,11,14,[18][19][20]) and Catalan (cf. [1,[4][5][6][7][9][10][11][13][14][15]19]) polynomials and numbers. Recently, Kim et al [11] introduced the Catalan-Daehee polynomials by means of the bosonic p-adic integrals and provided several interesting properties and relations.…”

“…The Catalan polynomials are defined by the following generating function (see [1,[4][5][6][7][9][10][11][13][14][15]19]):…”

A NOTE ON q-ANALOGUE OF CATALAN NUMBERS ASSOCIATED WITH q-CHANGHEE NUMBERS

“…As is well known, the Catalan numbers are defined by the generating function as follows (see [1,2,3,20,21,22,24,25,27])…”

Fully Degenerating of Daehee Numbers and Polynomials

“…Recently, many mathematicians as the systematic study of degenerate versions of some special polynomials and numbers (see , Kim et al [5], Khan et al [6][7][8], and Sharma et al [9]) have been established due to Carlitz's degenerate version of Bernoulli polynomials given by (see [10,11])…”