Symmetric Identities for Fubini Polynomials

Taekyun Kim,Dae Kim,Jongkyum Kwon,Gwan-Woo Jang

doi:10.3390/sym10060219

Abstract

We represent the generating function of w-torsion Fubini polynomials by means of a fermionic p-adic integral on Zp. Then we investigate a quotient of such p-adic integrals on Zp, representing generating functions of three w-torsion Fubini polynomials and derive some new symmetric identities for the w-torsion Fubini and two variable w-torsion Fubini polynomials.

Highlights

Introduction and PreliminariesIn recent years, various p-adic integrals on Z p have been used in order to find many interesting symmetric identities related to some special polynomials and numbers
Throughout our discussion, we will use the standard notations Z p, Q p, and C p to denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of the algebraic closure of Q p, respectively
The fermionic p-adic integral of f ( x ) on Z p was introduced by Kim as p N −1

Summary

Introduction

Various p-adic integrals on Z p have been used in order to find many interesting symmetric identities related to some special polynomials and numbers. They have been used by a good number of researchers in various contexts and especially in unfolding new interesting symmetric identities. The fermionic p-adic integral of f ( x ) on Z p was introduced by Kim (see [2]) as p N −1 Symmetry 2018, 10, 219 where En ( x ) are the usual Euler polynomials.

Results

Conclusion