Results 41 to 50 of about 207 (144)

Certain Properties and Characterizations of Two-Iterated Two-Dimensional Appell and Related Polynomials via Fractional Operators

Fractal and Fractional
This paper introduces the operational rule for 2-iterated 2D Appell polynomials and derives its generalized form using fractional operators. It also presents the generating relation and explicit forms that characterize the generalized 2-iterated 2D ...
Mohra Zayed, Shahid Ahmad Wani
doaj   +1 more source

On Appell-Vietoris Polynomials

In this paper we introduce a polynomial sequence (Vn(x))n≥0 involving the Vietoris’ number sequence and satisfying the Appell property. We derive several equivalent representations of Vn(x) and we deduce important relations closely related to the aforementioned Appell property.
Isabel Cação, M. Irene Falcão, Helmuth R. Malonek, Fernando Miranda, Graça Tomaz   +4 more
openaire   +2 more sources

On multiple Appell polynomials [PDF]

Proceedings of the American Mathematical Society, 2010
In this paper, we first define the multiple Appell polynomials and find several equivalent conditions for this class of polynomials. Then we give a characterization theorem that if multiple Appell polynomials are also multiple orthogonal, then they are the multiple Hermite polynomials.
openaire   +2 more sources

Classical Multiple Orthogonal Polynomials for Arbitrary Number of Weights and Their Explicit Representation

Studies in Applied Mathematics, Volume 154, Issue 3, March 2025.
ABSTRACT This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi–Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for general recurrence coefficients, as well as the stepline case, are provided for all these ...
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié‐Moreno, Manuel Mañas   +3 more
wiley   +1 more source

On a family of q-modified-Laguerre-Appell polynomials

Arab Journal of Basic and Applied Sciences
This paper aims to introduce a new class of special polynomials called q-modified Laguerre-Appell polynomials. Some definitions and concepts related to this class of polynomials, including generating function and series definition are explored.
Mohammed Fadel, Abdulghani Muhyi
doaj   +1 more source

Appell and Sheffer sequences: on their characterizations through functionals and examples

Comptes Rendus. Mathématique, 2021
The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the literature ...
Carrillo, Sergio A., Hurtado, Miguel
doaj   +1 more source

The Fueter-Sce mapping and the Clifford–Appell polynomials

Proceedings of the Edinburgh Mathematical Society, 2023
AbstractThe Fueter-Sce theorem provides a procedure to obtain axially monogenic functions, which are in the kernel of generalized Cauchy–Riemann operator in ${\mathbb{R}}^{n+1}$. This result is obtained by using two operators. The first one is the slice operator, which extends holomorphic functions of one complex variable to slice monogenic functions ...
De Martino, A, Diki, K, Adán, AG
openaire   +4 more sources

Orthogonal Laurent Polynomials of Two Real Variables

Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.
ABSTRACT In this paper, we consider an appropriate ordering of the Laurent monomials xiyj$x^{i}y^{j}$, i,j∈Z$i,j \in \mathbb {Z}$ that allows us to study sequences of orthogonal Laurent polynomials of the real variables x$x$ and y$y$ with respect to a positive Borel measure μ$\mu$ defined on R2$\mathbb {R}^2$ such that ({x=0}∪{y=0})∩supp(μ)=∅$(\lbrace ...
Ruymán Cruz‐Barroso, Lidia Fernández
wiley   +1 more source

On monomiality property of q-Gould-Hopper-Appell polynomials

Arab Journal of Basic and Applied Sciences
Recently, in the theory of q-special functions, the extension of the monomiality concept to q-special polynomials is introduced. This extension can be a beneficial tool for considering the quasi-monomiality of certain q-special polynomials.
Nusrat Raza, Mohammed Fadel, Subuhi Khan
doaj   +1 more source

Application of (q, τ)‐Bernoulli Interpolation to the Spectral Solution of Quantum Differential Equations

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
In order to solve fractional differential equations on quantum domains, this work provides a spectral approach based on higher‐order (q, τ)‐Bernoulli functions and polynomials. We build a robust basis for approximation in (q, τ)‐weighted Hilbert spaces by using the orthogonality properties of these extended polynomials and the Sheffer‐type generating ...
Shaher Momani, Rabha W. Ibrahim, Khalil Ezzinbi   +2 more
wiley   +1 more source