Results 1 to 10 of about 490,089 (251)

An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2008
We introduce the so-called Clifford-Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an ...
Hendrik De Bie
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Differential Equations Associated with Two Variable Degenerate Hermite Polynomials

Mathematics, 2020
In this paper, we introduce the two variable degenerate Hermite polynomials and obtain some new symmetric identities for two variable degenerate Hermite polynomials.
Kyung-Won Hwang, Cheon Seoung Ryoo
doaj   +2 more sources

On Apostol-Type Hermite Degenerated Polynomials

Mathematics, 2023
This article presents a generalization of new classes of degenerated Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi Hermite polynomials of level m.
Clemente Cesarano, William Ramírez, Stiven Díaz, Adnan Shamaoon, Waseem Ahmad Khan   +4 more
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Monomiality and a New Family of Hermite Polynomials [PDF]

Symmetry, 2022
The monomiality principle is based on an abstract definition of the concept of derivative and multiplicative operators. This allows to treat different families of special polynomials as ordinary monomials. The procedure underlines a generalization of the
G. Dattoli, S. Licciardi
semanticscholar   +3 more sources

Identities involving 3-variable Hermite polynomials arising from umbral method

Advances in Difference Equations, 2020
In this paper, we employ an umbral method to reformulate the 3-variable Hermite polynomials and introduce the 4-parameter 3-variable Hermite polynomials. We also obtain some new properties for these polynomials. Moreover, some special cases are discussed
Nusrat Raza, Umme Zainab, Serkan Araci, Ayhan Esi   +3 more
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Advancements in q-Hermite-Appell polynomials: a three-dimensional exploration

AIMS Mathematics
In this research, we leverage various $ q $-calculus identities to introduce the notion of $ q $-Hermite-Appell polynomials involving three variables, elucidating their formalism.
Mohra Zayed , Shahid Ahmad Wani, William Ramírez, Clemente Cesarano   +3 more
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On 2-variable q-Hermite polynomials

AIMS Mathematics, 2021
The quantum calculus has emerged as a connection between mathematics and physics. It has wide applications, particularly in quantum mechanics, analytic number theory, combinatorial analysis, operation theory etc.
Nusrat Raza, Mohammed Fadel , Kottakkaran Sooppy Nisar, M. Zakarya   +3 more
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Coefficient Estimates of New Families of Analytic Functions Associated with q-Hermite Polynomials

Axioms, 2023
In this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, we establish the bounds of the initial coefficients υ2, υ3, and υ4 of the Taylor–Maclaurin series and that of the Fekete–Szegö ...
Isra Al-shbeil, Adriana Cătaș, H. Srivastava, Najla M. Aloraini   +3 more
semanticscholar   +1 more source

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

Mathematics, 2023
A comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions.
M. Zayed, S. Wani, Yamilet Quintana
semanticscholar   +1 more source

Some relations satisfied by Hermite-Hermite matrix polynomials [PDF]

Mathematica Bohemica, 2017
The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula.
Ayman Shehata, Lalit Mohan Upadhyaya
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