The Multivariable Generalized Hermite-Type-Genocchi Polynomials of Order a

TL;DR

This paper introduces a new class of multivariable generalized Hermite-type-Genocchi polynomials of order a, exploring their properties, explicit forms, and connections to generalized Stirling numbers.

Contribution

It constructs and investigates a novel family of polynomials with explicit representations, addition formulas, and relationships to generalized Stirling numbers.

Findings

Derived explicit representations and addition formulas.

Established relationships with generalized Stirling numbers.

Analyzed fundamental properties of the new polynomial family.

Abstract

This study presents a new class of poly-Genocchi polynomials constructed through the integration of some interesting polynomials. The resulting family, referred to as the multivariable generalized Hermite-type-Genocchi polynomials of order a, is investigated in detail. Several fundamental properties are derived, including explicit representations, addition formulas, and polynomial expansions. In addition, relationships between this new family of polynomials and a certain generalized Stirling numbers of the first kind are established.