Results 81 to 90 of about 528 (133)

Certain Properties and Characterizations of Generalized Gould–Hopper-Based Hybrid Polynomials

Mathematics
This study offers a comprehensive generalization of the Gould–Hopper polynomials and their Appell-type analogs. Employing the quasi-monomiality approach, we delineate fundamental analytical characteristics, including recurrence relations, associated ...
Waseem Ahmad Khan, Francesco Aldo Costabile, Can Kızılateş, Khidir Shaib Mohamed, Alawia Adam, Mona A. Mohamed   +5 more
doaj   +1 more source

Sheffer and Non-Sheffer Polynomial Families

International Journal of Mathematics and Mathematical Sciences, 2012
By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials.
G. Dattoli, B. Germano, M. R. Martinelli, P. E. Ricci   +3 more
doaj   +1 more source

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

Differential Equation of Appell Polynomials Via the Factorization Method

, 2002
Let {Pn(x)}∞n=0 be a sequence of polynomials of degree n. We define two sequences of differential operators Φn and Ψn satisfying the following properties: By constructing these two operators for Appell polynomials, we determine their differential ...
He, Matthew, Ricci, P.E., Ricci, Paolo E., He, M.X.   +3 more
core   +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 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
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

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

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

Some properties of Appell type degenerate Bell polynomials

In recent years, the degenerate versions of some polynomial families such as Bernoulli, Euler, Apostol and Bell polynomials have been intensively studied in the literature.
ÇEKİM, BAYRAM, Özat, Zeynep, Özarslan, Mehmet Ali   +2 more
core   +1 more source