Certain Properties and Characterizations of Multivariable Hermite-Based Appell Polynomials via Factorization Method

Abstract

This paper introduces a new type of polynomials generated through the convolution of generalized multivariable Hermite polynomials and Appell polynomials. The paper explores several properties of these polynomials, including recurrence relations, explicit formulas using shift operators, and differential equations. Further, integrodifferential and partial differential equations for these polynomials are also derived. Additionally, the study showcases the practical applications of these findings by applying them to well-known polynomials, such as generalized multivariable Hermite-based Bernoulli and Euler polynomials. Thus, this research contributes to advancing the understanding and utilization of these hybrid polynomials in various mathematical contexts.

Keywords

• Appell polynomials
• multivariable Hermite polynomials
• recurrence relation
• shift operators
• differential equations
• applications