New formulae of products of the Frobenius-Euler polynomials

Yuan He,Sherry J Wang

doi:10.1186/1029-242x-2014-261

Abstract

In this paper, we perform a further investigation for the Frobenius-Euler polynomials. Some new formulae of products of the Frobenius-Euler polynomials are established by applying the generating function methods and some summation transform techniques. It turns out that some corresponding known results are obtained as special cases. MSC:11B68, 05A19.

Highlights

Let λ be a complex number with λ =
In [ ], Carlitz explored some formulae of products of the Frobenius-Euler polynomials and obtained that for non-negative integers m, n, Hm(x|λ)Hn(x|μ) λ(μ λμ
Motivated by the work of Carlitz [ ], in the present paper we establish some new formulae of products of the Frobenius-Euler polynomials by applying the generating function methods and some summation transform techniques

Summary

Introduction

Hn(λ) = Hn( |λ) are called the Frobenius-Euler numbers. For some interesting arithmetic properties of the Frobenius-Euler polynomials and numbers, one is referred to [ – ]. In [ ], Nielsen investigated three formulae of products of the classical Bernoulli and Euler polynomials. For further discoveries of Nielsen’s formulae on the classical Bernoulli and Euler polynomials, see [ – ] for details.

Results

Conclusion