Some identities of Frobenius-Euler polynomials arising from Frobenius-Euler basis

TL;DR

This paper derives new identities for Frobenius-Euler polynomials using their basis, and shows how these results relate to q-analogues and q-Bernstein polynomials, extending recent findings in the field.

Contribution

It introduces novel identities for Frobenius-Euler polynomials and connects them to q-analogues and q-Bernstein polynomials, expanding the theoretical framework.

Findings

New identities for Frobenius-Euler polynomials

Connections to q-analogues and q-Bernstein polynomials

Extension of recent results by Simsek et al.

Abstract

In this paper, we give some new and interesting identities which are derived from the basis of Frobenius-Euler. Recently, Simsek et als(see [13]) have given some identities of q-analogue of Frobenius-Euler polynomials related to q-Bernstein polynomials. From the methods of our paper, we can also derive the results and identities of Simsek et als (cf.[13]).