Identities involving Frobenius-Euler polynomials arising from non-linear differential equations

TL;DR

This paper explores non-linear differential equations linked to Frobenius-Euler polynomials, deriving new identities involving their sums and products, thus advancing the theoretical understanding of these special functions.

Contribution

It introduces novel identities between Frobenius-Euler polynomials and their higher-order counterparts derived from non-linear differential equations.

Findings

New identities between Frobenius-Euler polynomials and their higher-order forms

Relationships between generating functions and non-linear differential equations

Enhanced theoretical framework for Frobenius-Euler polynomials

Abstract

In this paper we consider non-linear differential equations which are closely related to the generating functions of Frobenius-Euler polynomials. From our non-linear differential equations, we derive some new identities between the sums of products of Frobenius-Euler polynomials and Frobenius-Euler polynomials of higher order.