Symmetry Identities of Changhee Polynomials of Type Two

Joohee Jeong,Seog-Hoon Rim,Dong-Jin Kang

doi:10.3390/sym10120740

Abstract

In this paper, we consider Changhee polynomials of type two, which are motivated from the recent work of D. Kim and T. Kim. We investigate some symmetry identities for the Changhee polynomials of type two which are derived from the properties of symmetry for the fermionic p-adic integral on Z p .

Highlights

Let p be a fixed odd prime number
By exploiting the method of fermionic p-adic integral on Z p, the Changhee polynomials of type two can be represented by the fermionic p-adic integrals of Z p : for t ∈ C p with | t | p < p
We investigate some symmetry identities for the w-Changhee polynomials of type two which are derived from the properties of symmetry for the fermionic p-adic integral on Z p

Summary

Introduction

Let p be a fixed odd prime number. Throughout this paper, Z p , Q p and C p will denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of the algebraic closure of Q p. The fermionic p-adic integral on Z p is defined by. Kim introduced the Changhee polynomials Ch type two by the generating function. By exploiting the method of fermionic p-adic integral on Z p , the Changhee polynomials of type two can be represented by the fermionic p-adic integrals of Z p : for t ∈ C p with | t | p < p. F n = Ch f n (0) are called the Changhee numbers of type two. We will introduce further generalization of Changhee polynomials of type two, by using again fermionic p-adic integration on Z p. We investigate some symmetry identities for the w-Changhee polynomials of type two which are derived from the properties of symmetry for the fermionic p-adic integral on Z p.

Changhee Polynomials and Numbers of Type Two

Symmetry of w-Changhee Polynomials of Type Two

Conclusions