New construction of type 2 degenerate central Fubini polynomials with their certain properties

Sunil Kumar Sharma,Waseem A Khan,Serkan Araci,Sameh S Ahmed

doi:10.1186/s13662-020-03055-4

Abstract

Kim et al. (Proc. Jangjeon Math. Soc. 21(4):589–598, 2018) have studied the central Fubini polynomials associated with central factorial numbers of the second kind. Motivated by their work, we introduce degenerate version of the central Fubini polynomials. We show that these polynomials can be represented by the fermionic p-adic integral on mathbb{Z}_{p}. From the fermionic p-adic integral equations, we derive some new properties related to degenerate central factorial numbers of the second kind and degenerate Euler numbers of the second kind.

Highlights

Let p be chosen as a fixed odd prime number
We make use of the following notations: Zp, Qp, Cp, N, N0 and R denote the ring of p-adic integers, the field of p-adic rational numbers, the completion of an algebraic closure of Qp, the set of natural number, the set of natural numbers containing zero and the set of real numbers, respectively
Kim et al [20] showed that the Fubini polynomials can be represented by the fermionic p-adic integral on Zp as follows: x 1 – et

Summary

Introduction

Let p be chosen as a fixed odd prime number. We make use of the following notations: Zp, Qp, Cp, N, N0 and R denote the ring of p-adic integers, the field of p-adic rational numbers, the completion of an algebraic closure of Qp, the set of natural number, the set of natural numbers containing zero and the set of real numbers, respectively. Kim et al [20] showed that the Fubini polynomials can be represented by the fermionic p-adic integral on Zp as follows: x 1 – et Carlitz [1] introduced the degenerate Bernoulli polynomials by means of the following generating function: Parallel to (6), the degenerate Euler polynomials are defined by means of the following generating function:

Results

Conclusion