Results 21 to 30 of about 972,343 (359)
Fast algorithms using orthogonal polynomials
Acta Numerica, 2020 We review recent advances in algorithms for quadrature, transforms, differential equations and singular integral equations using orthogonal polynomials.
S. Olver, R. Slevinsky, Alex Townsend
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On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle
Mathematics, 2020 In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials.
Lino G. Garza +2 more
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Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators [PDF]
, 2016 We consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types.
S. Odake
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Generalizations of orthogonal polynomials [PDF]
Journal of Computational and Applied Mathematics, 2005 AbstractWe give a survey of recent generalizations of orthogonal polynomials. That includes multidimensional (matrix and vector orthogonal polynomials) and multivariate versions, multipole (orthogonal rational functions) variants, and extensions of the orthogonality conditions (multiple orthogonality).
Bultheel, A. +4 more
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Journal of Approximation Theory, 1979 Abstract : Orthogonal polynomials satisfy a three term recurrence relation. The purpose of the paper is to give estimates for the orthogonal polynomials and the corresponding weight function provided that the coefficients in the recurrence formula behave in a prescribed manner. (Author)
Paul Nevai, Paul Nevai
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Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy [PDF]
, 2015 Given a matrix polynomial $W(x)$, matrix bi-orthogonal polynomials with respect to the sesquilinear form $\langle P(x),Q(x)\rangle_W=\int P(x) W(x)\operatorname{d}\mu(x)(Q(x))^{\top}$, $P(x),Q(x)\in\mathbb R^{p\times p}[x]$, where $\mu(x)$ is a matrix of
Carlos 'Alvarez-Fern'andez +4 more
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Zernike polynomials and their applications
Journal of Optics, 2022 The Zernike polynomials are a complete set of continuous functions orthogonal over a unit circle. Since first developed by Zernike in 1934, they have been in widespread use in many fields ranging from optics, vision sciences, to image processing. However,
Kuo Niu, Chao Tian
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Orthogonal Polynomials On Ellipses And Their Recurrence Relations
Demonstratio Mathematica, 2014 In this note we study the connection between orthogonal polynomials on an ellipse and orthogonal Laurent polynomials on the unit circle relative to some multiplicative measures and then establish the recurrence relations for orthogonal polynomials on an ...
Lauric Vasile
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Проблемы анализа, 2020 In this paper, we give the generating functions of binary product between 2-orthogonal Chebyshev polynomials and kFibonacci, k-Pell, k-Jacobsthal numbers and the other orthogonal Chebyshev polynomials.
H. Merzouk, B. Aloui, A. Boussayoud
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Symmetric orthogonal polynomials and the associated orthogonal 𝐿-polynomials [PDF]
Proceedings of the American Mathematical Society, 1995 We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function ( 1 + k
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