Certain Properties and Applications of Δh Hybrid Special Polynomials Associated with Appell Sequences

Alyusof, Rabab; Wani, Shahid Ahmad

doi:10.3390/fractalfract7030233

Cited by 9 publications

(8 citation statements)

References 11 publications

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“…For = 2, the first four two-variable Bell-based Stirling polynomials are as follows: Remark 4.2. When substituting y = 0 into the expression given by (4.1), we obtain a set of polynomials known as the Bell-Stirling polynomials of the second kind given by the expression: 1) .…”

Section: Fundingmentioning

confidence: 99%

“…Examples of special polynomials include well-known families such as Legendre polynomials, Chebyshev polynomials, Hermite polynomials, Bell polynomials, Touchard polynomials, Hermite polynomials and others. These polynomials often arise in mathematical physics, engineering, computer science, and other scientific disciplines, see for instance [1,3,4,6,8,[18][19][20]22].…”

Section: Introductionmentioning

confidence: 99%

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Properties and applications of Bell polynomials of two variables

Zayed,

Wani,

Ramirez

et al. 2024

J. Math. Computer Sci.

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In this article, we introduce Bell polynomials of two variables within the framework of generating functions and explore various properties associated with them. Specifically, we delve into explicit representations, summation formulae, recurrence relations, and addition formulas. Additionally, we present the matrix form and product formula for these polynomials. Finally, we introduce the two-variable Bell-based Stirling polynomials of the second kind and outline their corresponding results. This study contributes to a deeper understanding of the properties and applications of Bell polynomials in mathematical analysis.

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Section: Fundingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Properties and applications of Bell polynomials of two variables

Zayed,

Wani,

Ramirez

et al. 2024

J. Math. Computer Sci.

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“…In light of the identity presented in expression ( 7) of [15], we obtain the left-hand side of Equation (13). By denoting the right-hand side as…”

Section: Theorem 2 the Generating Expression For Mhfgps Denoted Asmentioning

confidence: 99%

“…The foundation for a more thorough understanding of the monomiality principle and its use in the context of hybrid special polynomials was laid by their combined contributions. According to studies like [10][11][12][13][14][15][16][17], unique categories of hybrid special polynomials connected to Appell sequences have been created and thoroughly investigated, endowing these polynomials with significant utility in a variety of domains. These areas cover engineering, biological sciences, medicine, and physical sciences, where these polynomials have important applications.…”

Section: Introductionmentioning

confidence: 99%

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

Wani,

Oros,

Mahnashi

et al. 2023

Mathematics

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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.

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“…As a consequence, the study of hybrid special polynomials has become a vibrant and dynamic area of research, with widespread applications in various disciplines such as physics, engineering, and computer science. Notably, recent breakthroughs utilizing the monomiality principle are evident in publications like [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Exploring the Characteristics of Δh Bivariate Appell Polynomials: An In-Depth Investigation and Extension through Fractional Operators

Almusawa

2024

Fractal Fract

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The objective of this article is to introduce the ∆h bivariate Appell polynomials ∆hAs[r](λ,η;h) and their extended form via fractional operators. The study described in this paper follows the line of study in which the monomiality principle is used to develop new results. It is further discovered that these polynomials satisfy various well-known fundamental properties and explicit forms. The explicit series representation of ∆h bivariate Gould–Hopper polynomials is first obtained, and, using this outcome, the explicit series representation of the ∆h bivariate Appell polynomials is further given. The quasimonomial properties fulfilled by bivariate Appell polynomials ∆h are also proved by demonstrating that the ∆h bivariate Appell polynomials exhibit certain properties related to their behavior under multiplication and differentiation operators. The determinant form of ∆h bivariate Appell polynomials is provided, and symmetric identities for the ∆h bivariate Appell polynomials are also exhibited. By employing the concept of the forward difference operator, operational connections are established, and certain applications are derived. Different Appell polynomial members can be generated by using appropriate choices of functions in the generating expression obtained in this study for ∆h bivariate Appell polynomials. Additionally, generating relations for the ∆h bivariate Bernoulli and Euler polynomials, as well as for Genocchi polynomials, are established, and corresponding results are obtained for those polynomials.

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Certain Properties and Applications of Δh Hybrid Special Polynomials Associated with Appell Sequences

Cited by 9 publications

References 11 publications

Properties and applications of Bell polynomials of two variables

Properties and applications of Bell polynomials of two variables

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

Exploring the Characteristics of Δh Bivariate Appell Polynomials: An In-Depth Investigation and Extension through Fractional Operators

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