Properties of Multivariable Hermite Polynomials in Correlation with Frobenius–Genocchi Polynomials

Shahid Ahmad Wani, Georgia Irina Oros (), Ali M. Mahnashi and Waleed Hamali
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Shahid Ahmad Wani: Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, Maharashtra, India
Georgia Irina Oros: Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania
Ali M. Mahnashi: Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
Waleed Hamali: Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia

Mathematics, 2023, vol. 11, issue 21, 1-17

Abstract: The evolution of a physical system occurs through a set of variables, and the problems can be treated based on an approach employing multivariable Hermite polynomials. These polynomials possess beneficial properties exhibited in functional and differential equations, recurring and explicit relations as well as symmetric identities, and summation formulae, among other examples. In view of these points, comprehensive schemes have been developed to apply the principle of monomiality from mathematical physics to various mathematical concepts of special functions, the development of which has encompassed generalizations, extensions, and combinations of other functions. Accordingly, this paper presents research on a novel family of multivariable Hermite polynomials associated with Frobenius–Genocchi polynomials, deriving the generating expression, operational rule, differential equation, and other defining characteristics for these polynomials. Additionally, the monomiality principle for these polynomials is verified, as well as establishing the series representations, summation formulae, operational and symmetric identities, and recurrence relations satisfied by these polynomials. This proposed scheme aims to provide deeper insights into the behavior of these polynomials and to uncover new connections between these polynomials, to enhance understanding of their properties.

Keywords: multivariable special polynomials; monomiality principle; explicit form; operational connection; symmetric identities; summation formulae; conjugates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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