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Orthogonal Polynomials on the Unit Circle
Encyclopedia of Special Functions: The Askey-Bateman Project, 2020ACubic Decompositionof Sequencesof Orthogonal Polynomialson the Unit Circle MANUEL ALFARO*, MARI¤A JOSE¤ CANTERO b,y and FRANCISCOMARCELLA¤ Nc,z Departamento de Matema¤ ticas,Universidad de Zaragoza, 50009 Zaragoza, Spain; Departamento de Matema¤ tica ...
Manuel Alfaroa
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Stochastic Duality and Orthogonal Polynomials
Springer Proceedings in Mathematics & statistics, 2017For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal polynomial) can
C. Franceschini, C. Giardinà
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Orthogonal Polynomials and Painlevé Equations
, 2017The Riemann-Hilbert formulation of orthogonal polynomials provides a crucial bridge between disparate areas of mathematics, allowing tools developed in the context of integrable systems to be available for the study of orthogonal polynomials and random ...
W. Assche
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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
, 2000Riemann-Hilbert problems Jacobi operators Orthogonal polynomials Continued fractions Random matrix theory Equilibrium measures Asymptotics for orthogonal polynomials Universality Bibliography.
P. Deift
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On the Orthogonality of Classical Orthogonal Polynomials
Integral Transforms and Special Functions, 2003We consider the orthogonality of rational functions W n ( s ) as the Laplace transform images of a set of orthoexponential functions, obtained from the Jacobi polynomials, and as the Laplace transform images of the Laguerre polynomials. We prove that the orthogonality of the Jacobi and the Laguerre polynomials is induced by the orthogonality of the ...
Miomir S. Stanković +1 more
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2022
In this chapter, we give an overview of the links between Riordan arrays and orthogonal polynomials, and then we study some specialized areas including classical and semi-classical orthogonal polynomials defined by Riordan arrays, orthogonal polynomials that can be described as the moment sequences of Riordan arrays, applications of exponential Riordan
Shapiro L. +6 more
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In this chapter, we give an overview of the links between Riordan arrays and orthogonal polynomials, and then we study some specialized areas including classical and semi-classical orthogonal polynomials defined by Riordan arrays, orthogonal polynomials that can be described as the moment sequences of Riordan arrays, applications of exponential Riordan
Shapiro L. +6 more
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The Classical Orthogonal Polynomials
, 2015This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have.The first chapter defines the ...
B. Doman
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Journal of The Optical Society of America A-optics Image Science and Vision, 2014
Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They
Jingfei Ye +5 more
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Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They
Jingfei Ye +5 more
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1966
Publisher Summary This chapter focuses on simple sets of orthogonal polynomials. These sets of polynomials arise in various ways, one of which is as the solutions of a class of differential equations. It has been shown that, under certain conditions, given any interval and a positive weight function on that interval, there exists a corresponding set ...
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Publisher Summary This chapter focuses on simple sets of orthogonal polynomials. These sets of polynomials arise in various ways, one of which is as the solutions of a class of differential equations. It has been shown that, under certain conditions, given any interval and a positive weight function on that interval, there exists a corresponding set ...
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A Conjecture on Exceptional Orthogonal Polynomials
Foundations of Computational Mathematics, 2012Exceptional orthogonal polynomial systems (X-OPSs) arise as eigenfunctions of Sturm–Liouville problems, but without the assumption that an eigenpolynomial of every degree is present.
D. Gómez‐Ullate, N. Kamran, R. Milson
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