Results 41 to 50 of about 56,667 (302)
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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q-Hermite Polynomials and Classical Orthogonal Polynomials [PDF]
Canadian Journal of Mathematics, 1996 AbstractWe use generating functions to express orthogonality relations in the form of q-beta. integrals. The integrand of such a q-beta. integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials ...
Christian Berg, Mourad E. H. Ismail
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Discrete semi-classical orthogonal polynomials of class one on quadratic lattices
Journal of difference equations and applications (Print), 2018 We study orthogonal polynomials on quadratic lattices with respect to Stieltjes functions, S, that satisfy a difference equation where A is a polynomial of degree less or equal than 3 and C is a polynomial of degree greater or equal than 1 and less or ...
G. Filipuk, M. N. Rebocho
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On a new characterization of the classical orthogonal polynomials
Journal of Approximation Theory, 1992 AbstractIn this paper we give a new characterization of the classical orthogonal polynomials (Jacobi, Laguerre, and Hermite polynomials) by a special property of the sequences in their recurrence formula. The results also allow an easy derivation of the asymptotic distribution of the zeros of the classical orthogonal polynomials.
Holger Dette, W. J. Studden
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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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Krylov complexity and orthogonal polynomials
Nuclear Physics B, 2022 Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method.
Wolfgang Mück, Yi Yang
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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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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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Point vortices and classical orthogonal polynomials [PDF]
Regular and Chaotic Dynamics, 2012 Stationary equilibria of point vortices with arbitrary choice of circulations in a background flow are studied. Differential equations satisfied by generating polynomials of vortex configurations are derived. It is shown that these equations can be reduced to a single one.
Nikolai A. Kudryashov, Maria V. Demina
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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