Families of Differential Equations Associated with The Generalized 1-Parameter 3-Variable Hermite–Frobenius–Euler Polynomials

Abstract

This paper presents a novel framework for introducing generalized 1-parameter 3-variable Hermite–Frobenius–Euler polynomials. These polynomials are characterized by generating functions, series definitions, and summation formulae, elucidating their fundamental properties. Moreover, the study establishes recurrence relations, shift operators, and various differential equations, including differential, integro-differential, and partial differential equations, utilizing a factorization method.