Results 51 to 60 of about 132,731 (333)
$q$-Classical orthogonal polynomials: A general difference calculus approach
, 2009 It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator.
A.F. Nikiforov +26 more
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New Formulas and Connections Involving Euler Polynomials
Axioms, 2022 The major goal of the current article is to create new formulas and connections between several well-known polynomials and the Euler polynomials. These formulas are developed using some of these polynomials’ well-known fundamental characteristics as well
Waleed Mohamed Abd-Elhameed +1 more
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CHARACTERIZATION OF POLYNOMIALS VIA A RAISING OPERATOR
Проблемы анализа, 2023 This paper investigates a first-order linear differential operator 𝒥𝜉, where 𝜉 = (𝜉1, 𝜉2)\in (C^2\(0,0), and 𝐷 := 𝑑/𝑑𝑥. The operator is defined as 𝒥𝜉 := 𝑥(𝑥𝐷+ I) + 𝜉1 I + 𝜉2𝐷, with I representing the identity on the space of polynomials with complex ...
Jihad Souissi
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Duality for classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 2005 Some aspects of duality for the classical orthogonal polynomials named after Laguerre and Jacobi are explained. The Laguerre polynomials form a limit case of the discrete Meixner polynomials. A certain integral identity involving Laguerre polynomials can be obtained as a limiting case of an identity involving Meixner polynomials.
openaire +2 more sources
New characterizations of classical orthogonal polynomials
Indagationes Mathematicae, 1996 The authors reconsider the classical orthogonal polynomials (i.e., Jacobi, Laguerre, Hermite and Bessel polynomials) and give some new characterizations of them. The results are expressed in the form of two theorems which claim that some statements are equivalent to each other.
Kil Hyun Kwon +8 more
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Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
, 2004 The Ruijsenaars-Schneider systems are `discrete' version of the Calogero-Moser (C-M) systems in the sense that the momentum operator p appears in the Hamiltonians as a polynomial in e^{\pm\beta' p} (\beta' is a deformation parameter) instead of an ...
Andrews G E +29 more
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Parameter Derivatives of the Jacobi Polynomials with Three Variables on the Simplex
MATEC Web of Conferences, 2016 In this paper, an attempt has been made to derive parameter derivatives of Jacobi polynomials with three variables on the simplex. They are obtained via parameter derivatives of the classical Jacobi polynomials Pn(α,β)(x) with respect to their parameters.
Aktaş Rabia
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Mathematics, 2018 This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim +3 more
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Extensions of discrete classical orthogonal polynomials beyond the orthogonality
Journal of Computational and Applied Mathematics, 2009 It is well known that the family of Hahn polynomials $\{h_n^{ , }(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $ $-Sobolev orthogonality.
Costas-Santos, Roberto S. +1 more
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Computational Modeling of Reticular Materials: The Past, the Present, and the Future
Advanced Materials, EarlyView.Reticular materials are advanced materials with applications in emerging technologies. A thorough understanding of material properties at operating conditions is critical to accelerate the deployment at an industrial scale. Herein, the status of computational modeling of reticular materials is reviewed, supplemented with topical examples highlighting ...
Wim Temmerman +3 more
wiley +1 more source