Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials

Mohra Zayed, Shahid Ahmad Wani () and Yamilet Quintana ()
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Mohra Zayed: Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Shahid Ahmad Wani: Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Lavale, Pune 412115, Maharashtra, India
Yamilet Quintana: Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, 28911 Madrid, Spain

Mathematics, 2023, vol. 11, issue 16, 1-17

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.

Keywords: multivariate special polynomials; monomiality principle; explicit form; operational connection; symmetric identities; summation formulae (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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