Certain properties and characteristics of extended multivariate Hermite-Frobenius Euler polynomials of $1$-parameter

Abstract

This paper investigates a new class of the extended multivariate Hermite-Frobenius Euler polynomials of one-parameter ($EMHFEP$ of $1$-parameter), focusing on their structural and analytical features. By utilizing series representations and generating functions, key properties and an associated operational framework are established.  Additionally, various differential, integrodifferential, and partial differential equations satisfied by these polynomials are presented. Several summation formulas are introduced, enhancing their computational applicability.