Laguerre–Freud Equations for the Gauss Hypergeometric Discrete Orthogonal Polynomials [PDF]
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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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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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 ...
Galina Filipuk +2 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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Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials [PDF]
Mathematics, 2020 In this paper, we consider a discrete Sobolev inner product involving the Jacobi weight with a twofold objective. On the one hand, since the orthonormal polynomials with respect to this inner product are eigenfunctions of a certain differential operator,
Juan F. Mañas-Mañas +2 more
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Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices [PDF]
, 2000 We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number.
Дмитрий Александрович Лейтес +1 more
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Exactly solvable discrete quantum mechanical systems and multi-indexed orthogonal polynomials of the continuous Hahn and Meixner–Pollaczek types [PDF]
, 2019 We present new exactly solvable systems of the discrete quantum mechanics with pure imaginary shifts, whose physical range of the coordinate is the whole real line.
Satoru Odake
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Discrete Transforms and Orthogonal Polynomials of (Anti)Symmetric Multivariate Cosine Functions [PDF]
, 2014 The discrete cosine transforms of types V--VIII are generalized to the antisymmetric and symmetric multivariate discrete cosine transforms. Four families of discretely and continuously orthogonal Chebyshev-like polynomials corresponding to the ...
Jiří Hrivnák, Lenka Motlochová
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Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts [PDF]
, 2017 In our previous papers, the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials and the Casoratian identities for the Askey-Wilson polynomial and its reduced form polynomials were presented.
Odake, Satoru
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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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