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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Pearson equations for discrete orthogonal polynomials: III—Christoffel and Geronimus transformations [PDF]
RACSAM, 2021 Contiguous hypergeometric relations for semiclassical discrete orthogonal polynomials are described as Christoffel and Geronimus transformations.
Manuel Mañas
semanticscholar +3 more sources
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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Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices [PDF]
, 2005 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.
A. F. Nikiforov +15 more
core +2 more sources
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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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.
S. Odake
semanticscholar +6 more sources
Unique positive solutions to q-discrete equations associated with orthogonal polynomials [PDF]
Journal of difference equations and applications (Print), 2020 Boelen et al. [q-discrete Painlevé equations for recurrence coefficients of modified q-Freud orthogonal polynomials, J. Differ. Equ. Appl. 16(1) (2010), pp.
Tomas Lasic Latimer
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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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New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials
Mathematics, 2020 A new criterion for Schur stability is derived by using basic results of the theory of orthogonal polynomials. In particular, we use the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation ...
Luis E. Garza +2 more
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Laguerre–Freud equations for three families of hypergeometric discrete orthogonal polynomials [PDF]
Studies in applied mathematics (Cambridge), 2022 The Cholesky factorization of the moment matrix is considered for discrete orthogonal polynomials of hypergeometric type. We derive the Laguerre–Freud equations when the first moments of the weights are given by the 1F2, 2F2, and 3F2 generalized ...
Itsaso Fern'andez-Irisarri +1 more
semanticscholar +1 more source