Properties of multivariate Hermite polynomials in correlation with Frobenius-Euler polynomials Articles uri icon

publication date

  • August 2023

issue

  • 16

volume

  • 11

International Standard Serial Number (ISSN)

  • 2227-7390

abstract

  • A comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions. This paper presents research on a novel family of multivariate Hermite polynomials associated with Apostol-type Frobenius┬┐Euler polynomials. The study derives the generating expression, operational rule, differential equation, and other defining characteristics for these polynomials. Additionally, the monomiality principle for these polynomials is verified. Moreover, the research establishes series representations, summation formulae, and operational and symmetric identities, as well as recurrence relations satisfied by these polynomials.

subjects

  • Mathematics

keywords

  • multivariate special polynomials; monomiality principle; explicit form; operational connection; symmetric identities; summation formulae