Results 31 to 40 of about 103 (90)

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

Controllability and Modeling Perspectives of Tempered Ψ‐Caputo Fractional Systems

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this article, we investigated the controllability of fractional dynamical systems (FDS) involving the tempered Ψ‐Caputo fractional derivative (FD). First, we derived the solution representation for this generalized FD with the help of Laplace transform and Mittag–Leffler (M‐L) function.
Inzamamul Haque, Mohammad Ayman-Mursaleen, Hojjatollah Amiri Kayvanloo, Smritijit Sen   +3 more
wiley   +1 more source

Finding identities and q-difference equations for new classes of bivariate q-matrix polynomials

Applied Mathematics in Science and Engineering
This article introduces 2-variable q-Hermite matrix polynomials and delves into their complex representation, unravelling specific outcomes. The exploration encompasses the derivation of insightful identities for the q-cosine and q-sine analogues of the ...
Subuhi Khan, Hassan Ali, Mohammed Fadel
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

Multiple Binomial‐Type Operators and Their Approximation Properties

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we introduce multiple binomial‐type operators (multiple Bernstein–Sheffer operators) and investigate their approximation properties. These properties are analyzed by means of a Korovkin‐type theorem. Furthermore, by using the first and second modulus of continuity together with Peetre’s κ‐functional, we establish the rate of convergence ...
Mehmet Ali Özarslan, Bayram Çekim, Sezin Çit, Smritijit Sen   +3 more
wiley   +1 more source

Poisson kernels of q$q$‐3D Hermite polynomials expansion for functions of several variables via generalized q$q$‐heat equations

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
wiley   +1 more source

A $q$-Umbral Approach to $q$-Appell Polynomials

, 2015
In this paper we aim to specify some characteristics of the so called family of $q$-Appell Polynomials by using $q$-Umbral calculus. Next in our study, we focus on $q$-Genocchi numbers and polynomials as a famous member of this family. To do this, firstly we show that any arbitrary polynomial can be written based on a linear combination of $q$-Genocchi
Keleshteri, Marzieh Eini, Mahmudov, Nazim I.   +1 more
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

A Study of the q-Truncated Exponential–Appell Polynomials

Mathematics
This article introduces the 2-variable q-truncated exponential–Appell (q-trunc. exp. Appell) polynomials and investigates their fundamental properties. Specific results are derived for the q-trunc. exp.
Francesco Aldo Costabile, Subuhi Khan, Hassan Ali   +2 more
doaj   +1 more source

Densely generated 2D q-Appell polynomials of Bessel type and q-addition formulas

Boletim da Sociedade Paranaense de Matemática, 2022
The article aims to introduce a densely generated class of $2D$ $q$-Appell polynomials of Bessel type via generating equation and to establish its $q$-determinant form. It is advantageous to consider the $2D$ $q$-Bernoulli, $2D$ $q$-Roger Szeg\"{o} and $2D$ $q$-Al-Salam Carlitz polynomials of Bessel type as their special members.
openaire   +4 more sources