A note on the new q-extension of Frobenius-Euler numbers and polynomials

TL;DR

This paper introduces a new q-extension of Frobenius-Euler numbers and polynomials, deriving identities based on their orthogonality properties and proposing an open question about their orthogonality.

Contribution

It presents a novel q-extension of Frobenius-Euler numbers and polynomials, along with derived identities and an open problem on their orthogonality.

Findings

Derived new identities from orthogonality properties

Proposed an open question on orthogonality of the polynomials

Extended classical Frobenius-Euler numbers with a q-parameter

Abstract

In this paper, we consider the new q-extension of Frobenius-Euler numbers and polynomials and we derive some interesting identities from the orthogonality type properties for the new q-extension of Frobenius-Euler polynomials. Finally we suggest one open question related to orthogonality of polynomials.