Results 61 to 70 of about 207 (144)

Rational solutions of the fifth Painlevé equation. Generalized Laguerre polynomials

Studies in Applied Mathematics, Volume 152, Issue 1, Page 453-507, January 2024.
Abstract In this paper, rational solutions of the fifth Painlevé equation are discussed. There are two classes of rational solutions of the fifth Painlevé equation, one expressed in terms of the generalized Laguerre polynomials, which are the main subject of this paper, and the other in terms of the generalized Umemura polynomials. Both the generalized
Peter A. Clarkson, Clare Dunning
wiley   +1 more source

Sequences of twice-iterated Δw-Gould–Hopper Appell polynomials

Journal of Taibah University for Science
In this paper, we introduce general sequence of twice-iterated [Formula: see text]-(degenerate) Gould–Hopper Appell polynomials (TI-DGHAP) via discrete [Formula: see text]-Gould–Hopper Appell convolution. We obtain some of their characteristic properties
Neslihan Biricik, Bayram Çekim, Mehmet Ali Özarslan   +2 more
doaj   +1 more source

The relation of the d-orthogonal polynomials to the Appell polynomials

Journal of Computational and Applied Mathematics, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

The telephone polynomials: An Appell-type orthogonal polynomials connecting Hermite–Laguerre polynomials

Nuclear Physics B
This article investigates a new Appell-type sequence, the telephone polynomials, which extend the classical telephone (involution) numbers. We present their fundamental algebraic properties, structural characterizations, and diverse interconnections with
Kalika Prasad, Munesh Kumari
doaj   +1 more source

Some properties of generalized hypergeometric Appell polynomials

Karpatsʹkì Matematičnì Publìkacìï, 2020
Let $x^{(n)}$ denotes the Pochhammer symbol (rising factorial) defined by the formulas $x^{(0)}=1$ and $x^{(n)}=x(x+1)(x+2)\cdots (x+n-1)$ for $n\geq 1$.
L. Bedratyuk, N. Luno
doaj   +1 more source

Finding the q-Appell Convolution of Certain Polynomials Within the Context of Quantum Calculus

Mathematics
This article introduces the theory of three-variable q-truncated exponential Gould–Hopper-based Appell polynomials by employing a generating function approach that incorporates q-calculus functions.
Waseem Ahmad Khan, Khidir Shaib Mohamed, Francesco Aldo Costabile, Can Kızılateş, Cheon Seoung Ryoo   +4 more
doaj   +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

Two-iterated degenerate Appell polynomials: properties and applications

Arab Journal of Basic and Applied Sciences
In the development of hybrid special polynomials, it is essential to incorporate the monomiality principle, operational rules, and other related properties.
Shahid Ahmad Wani
doaj   +1 more source

Fractional Operator Approach and Hybrid Special Polynomials: The Generalized Gould–Hopper–Bell-Based Appell Polynomials and Their Characteristics

Fractal and Fractional
This study introduces a novel generalized class of special polynomials using a fractional operator approach. These polynomials are referred to as the generalized Gould–Hopper–Bell-based Appell polynomials.
Rabeb Sidaoui, E. I. Hassan, Abdulghani Muhyi, Khaled Aldwoah, A. H. A. Alfedeel, Khidir Shaib Mohamed, Alawia Adam   +6 more
doaj   +1 more source

Noncentral Limit Theorems and Appell Polynomials

The Annals of Probability, 1987
Let \(n\geq 1\) be an integer and \(\{\xi_ i\}^{\infty}_{i=-\infty}\) an i.i.d. sequence of random variables with mean 0 and E \(\xi\) \({}_ i^{2n}
Avram, Florin, Taqqu, Murad S.
openaire   +2 more sources