Results 81 to 90 of about 207 (144)

A characterization of the Rogers q-hermite polynomials

International Journal of Mathematics and Mathematical Sciences, 1995
In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also 𝒟q-Appell where 𝒟q is the Askey-Wilson finite difference operator.
Waleed A. Al-Salam
doaj   +1 more source

Investigating Multidimensional Degenerate Hybrid Special Polynomials and Their Connection to Appell Sequences: Properties and Applications

Axioms
This paper explores the operational principles and monomiality principles that significantly shape the development of various special polynomial families.
Awatif Muflih Alqahtani, Saleem Yousuf, Shahid Ahmad Wani, Roberto S. Costas-Santos   +3 more
doaj   +1 more source

ON THE STRUCTURE OF 𝐷_𝑊 -APPELL DUNKL CLASSICAL ORTHOGONAL POLYNOMIALS

Проблемы анализа
In this paper, we investigate a class of classical orthogonal polynomials associated with the 𝐷_𝑤-Dunkl operator. This class is defined via a lowering operator that combines the discrete translation operator with a reflection-invariant component.
J. Souissi, K. A. Alanezy
doaj   +1 more source

On Generalized Class of Bell Polynomials Associated with Geometric Applications

Axioms
In this paper, we introduce a new class of special polynomials called the generalized Bell polynomials, constructed by combining two-variable general polynomials with two-variable Bell polynomials. The concept of the monomiality principle was employed to
Rashad A. Al-Jawfi, Abdulghani Muhyi, Wadia Faid Hassan Al-shameri   +2 more
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Appell polynomials and their relatives

, 2003
45 pages, 2 postscript ...
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Exploring a Novel Family of Appell Polynomials Associated with Gould–Hopper–Fubini Polynomials

Mathematics
In this paper, we establish a new hybrid class of special polynomials, the Gould–Hopper–Fubini-based Appell polynomials. Using the monomiality principle, we derive their generating function and explore related properties and identities.
F. Gassem, Abdulghani Muhyi, Hadeel Arwah, Habeeb Ibrahim, Khaled Aldwoah, Amer Alsulami, Mohammed Rabih   +6 more
doaj   +1 more source

Laguerre-type general-Appell polynomials

Integral Transforms and Special Functions
In this paper, new and general form of Laguerre-type Appell polynomials are introduced by using the Laguerre-type exponential function. For this new polynomial family, we present explicit representation, recurrence relation, lowering and raising operators, differential equation, determinant representation and some other properties.
Zeynep Özat, Bayram Çekim, Mehmet Ali Özarslan   +2 more
openaire   +3 more sources

Extended forms of Legendre-Laguerre-based hybrid polynomials and their characteristics via fractional operator approach

Journal of Inequalities and Applications
This study presents an extensive generalization of Legendre–Laguerre polynomials along with their Appell-type counterparts. Using the quasi-monomiality approach, we establish core analytical features, including recurrence relations, associated ...
Waseem Ahmad Khan, Shahid Ahmad Wani, Mohammad Ayman-Mursaleen, Ketan Kotecha, Prakash Jadhav   +4 more
doaj   +1 more source

On Appell Polynomials [PDF]

Proceedings of the American Mathematical Society, 1951
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A New Generalization of Legendre-Based Appell Polynomials with Two Parameters and Their Applications

Axioms
In the present work, we introduce and study a new two-parameter generalization of Legendre-based Appell polynomials, defined through an explicit representation that unifies classical Legendre structures with the Appell polynomial framework. Starting from
Ghaliah Alhamzi, Georgia Irina Oros, Mdi Begum Jeelani, Kalika Prasad, Shahid Ahmad Wani   +4 more
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