Pearson equations for discrete orthogonal polynomials: III—Christoffel and Geronimus transformations [PDF]
RACSAM, 2022 Contiguous hypergeometric relations for semiclassical discrete orthogonal polynomials are described as Christoffel and Geronimus transformations.
Manuel Mañas
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Laguerre–Freud Equations for the Gauss Hypergeometric Discrete Orthogonal Polynomials
Mathematics, 2023 The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials. This family of discrete orthogonal polynomials has a weight with first moment given by ρ0=2F1a,bc+1;η.
Itsaso Fernández-Irisarri +1 more
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A General Method for Generating Discrete Orthogonal Matrices [PDF]
IEEE Access, 2021 Discrete orthogonal matrices have applications in information coding and cryptography. It is often challenging to generate discrete orthogonal matrices.
Ka-Hou Chan, Wei Ke, Sio-Kei Im
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Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (
Hiroshi Miki +2 more
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Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second order differential ...
G. Filipuk, W. Assche
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Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations [PDF]
Journal of Physics A: Mathematical and Theoretical, 2020 Over the last decade it has become clear that discrete Painlevé equations appear in a wide range of important mathematical and physical problems. Thus, the question of recognizing a given non-autonomous recurrence as a discrete Painlevé equation and ...
Anton Dzhamay +2 more
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Differential equations for discrete Laguerre–Sobolev orthogonal polynomials [PDF]
, 2014 The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Jacobi-Sobolev bilinear form with mass point at −1 and/or +1.
Antonio J. Durán +1 more
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Discrete Transforms and Orthogonal Polynomials of (Anti)symmetric Multivariate Sine Functions
Entropy, 2018 Sixteen types of the discrete multivariate transforms, induced by the multivariate antisymmetric and symmetric sine functions, are explicitly developed. Provided by the discrete transforms, inherent interpolation methods are formulated.
Adam Brus +2 more
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From Krall discrete orthogonal polynomials to Krall polynomials [PDF]
Journal of Mathematical Analysis and Applications, 2017 We show how to get Krall polynomials from Krall discrete polynomials using a procedure of passing to the limit in some of the parameters of the family. We also show that this procedure has to be different to the standard one used in the Askey scheme to go from the classical discrete polynomials to the classical polynomials.
Antonio J. Durán
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Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions [PDF]
Transactions of the American Mathematical Society, 2019 The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalized to discrete settings involving either a linear or an exponential lattice. The corresponding correlation functions can be expressed in terms of
Peter J. Forrester, Shi‐Hao Li
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