Explicit expression for symmetric identities of w-Catalan–Daehee polynomials

Abstract

Recently, Catalan-Daehee numbers are studied by several authors. In this paper, we consider the w-Catalan-Daehee polynomials and investigate some properties for those polynomials. In addition, we give explicit expression for the symmetric identities of the w-Catalan-Daehee polynomials which are derived from p-adic invariant integral on Z p .

Symmetry Identities of Changhee Polynomials of Type Two

“…For the cases of w = 1, w = 1 2 and w = 1 4 , the symmetry of the w-Changhee polynomials of type two are related to the works of Changhee polynomials of type two, those of well-known Changhee polynomials (see [4,22]), and those of the Catalan polynomials (see [20]) respectively.…”

“…Recently, many works are done on some identities of special polynomials in the view point of degenerate sense (see [15,20,21]). Our result could be developed in that direction also: i.e., on the symmetry of the degenerate w-Changhee polynomials of type two.…”

“…Motivated from D. Kim and T. Kim [20], for w ∈ N, we define w-Changhee polynomials of type two by the following generating function…”

Some Identities for the Two Variable Fubini Polynomials

“…and used the fermionic p-adic integral on Z p described in [4] to give some similar symmetric identities for the ω-torsion Fubini polynomials to the ones stated in [5][6][7]. In particular, they showed that for non-negative integer n and positive integers ω 1 , ω 2 such that ω 1 ≡ 1 (mod 2) and ω 2 ≡ 1 (mod 2),…”

SYMMETRY IDENTITIES OF CHANGHEE POLYNOMIALS OF TYPE TWO

“…Motivated from Kim and Kim [2], for w ∈ N, we define w-torsion Changhee polynomials of type two by the following generating function…”