Results 71 to 80 of about 2,589 (160)

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

Exploring the Characteristics of Δ_h Bivariate Appell Polynomials: An In-Depth Investigation and Extension through Fractional Operators

Fractal and Fractional
The objective of this article is to introduce the ∆h bivariate Appell polynomials ∆hAs[r](λ,η;h) and their extended form via fractional operators. The study described in this paper follows the line of study in which the monomiality principle is used to ...
Musawa Yahya Almusawa
doaj   +1 more source

Appell polynomials and their relatives II. Boolean theory

, 2007
The Appell-type polynomial family corresponding to the simplest non-commutative derivative operator turns out to be connected with the Boolean probability theory, the simplest of the three universal non-commutative probability theories (the other two ...
Anshelevich, Michael
core   +2 more sources

Truncated-Exponential-Based General-Appell Polynomials

Mathematics
In this paper, a new and general form of truncated-exponential-based general-Appell polynomials is introduced using the two-variable general-Appell polynomials.
Zeynep Özat, Bayram Çekim, Mehmet Ali Özarslan, Francesco Aldo Costabile   +3 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

A New Generalization of mth-Order Laguerre-Based Appell Polynomials Associated with Two-Variable General Polynomials

Mathematics
This paper presents a novel generalization of the mth-order Laguerre and Laguerre-based Appell polynomials and examines their fundamental properties. By establishing quasi-monomiality, we derive key results, including recurrence relations, multiplicative
Waseem Ahmad Khan, Khidir Shaib Mohamed, Francesco Aldo Costabile, Shahid Ahmad Wani, Alawia Adam   +4 more
doaj   +1 more source

On hypergeometric Bernoulli numbers and polynomials [PDF]

, 2015
In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.Comment: 12 ...
Hu, Su, Kim, Min-Soo
core  

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

Degenerate 2D bivariate Appell polynomials: properties and applications

Applied Mathematics in Science and Engineering, 2023
The development of certain aspects of hybrid special polynomials after incorporating monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable.
Shahid Ahmad Wani, Arundhati Warke, Javid Gani Dar   +2 more
doaj   +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