Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations [PDF]
Studies in applied mathematics (Cambridge), 2021 The Cholesky factorization of the moment matrix is applied to discrete orthogonal polynomials on the homogeneous lattice. In particular, semiclassical discrete orthogonal polynomials, which are built in terms of a discrete Pearson equation, are studied ...
Manuel Mañas +2 more
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Discrete Painlevé equations for recurrence coefficients of Laguerre–Hahn orthogonal polynomials of class one [PDF]
, 2016 G. Filipuk, M. N. Rebocho
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Comparative asymptotics for discrete semiclassical orthogonal polynomials
Bulletin of Mathematical Sciences, 2023 We study the ratio [Formula: see text] asymptotically as [Formula: see text], where the polynomials [Formula: see text] are orthogonal with respect to a discrete linear functional and [Formula: see text] denote the falling factorial polynomials.
Diego Dominici
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Coherent Dynamics of Quantum Systems with Non-Uniform Fourier Space Excited by Laser Radiation
Zanco Journal of Pure and Applied Sciences, 2022 The algorithm is presented to solve dynamical equations for excitation of molecular models with multiple energy levels. It uses only discrete structures: discrete orthogonal polynomials constructed specially in Fourier space of the probability amplitudes,
Sary Banjak , Vadim Savva
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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, 2019 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 ...
A. Dzhamay, G. Filipuk, Alexander Stokes
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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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Mathematics, 2023 This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogs of Pascal distributions on a legged star-like set.
Jorge Arvesú +1 more
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Gottlieb Polynomials and Their q-Extensions
Mathematics, 2021 Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles.
Esra ErkuŞ-Duman, Junesang Choi
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Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials
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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Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point [PDF]
, 2014 In this paper, we develop the Riemann–Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an accumulation point.
Xiao-Bo Wu +3 more
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