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
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
semanticscholar +1 more source
Moments of discrete orthogonal polynomial ensembles [PDF]
Electronic Journal of Probability, 2020 20 ...
Cohen, Philip +2 more
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Discrete Painlevé equations for recurrence coefficients of Laguerre–Hahn orthogonal polynomials of class one [PDF]
, 2016 Galina Filipuk, M.N. Rebocho
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Discrete Entropies of Orthogonal Polynomials [PDF]
Constructive Approximation, 2008 Let $p_n$ be the $n$-th orthonormal polynomial on the real line, whose zeros are $ _j^{(n)}$, $j=1, ..., n$. Then for each $j=1, ..., n$, $$ \vec _j^2 = ( _{1j}^2, ..., _{nj}^2) $$ with $$ _{ij}^2= p_{i-1}^2 ( _j^{(n)}) (\sum_{k=0}^{n-1} p_k^2( _j^{(n)}))^{-1}, \quad i=1, >..., n, $$ defines a discrete probability distribution. The Shannon
Aptekarev, A. I. +3 more
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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
doaj +1 more source
Advanced Materials Interfaces, EarlyView., 2023 This review discusses the use of Surface‐Enhanced Raman Spectroscopy (SERS) combined with Artificial Intelligence (AI) for detecting antimicrobial resistance (AMR). Various SERS studies used with AI techniques, including machine learning and deep learning, are analyzed for their advantages and limitations.
Zakarya Al‐Shaebi +4 more
wiley +1 more source
Discrete Orthogonality Relations for the Multi-Indexed Orthogonal Polynomials in Discrete Quantum Mechanics with Pure Imaginary Shifts [PDF]
J. Math. Phys. 64 (2023) 053503 (21pp), 2021 The discrete orthogonality relations for the multi-indexed orthogonal polynomials in discrete quantum mechanics with pure imaginary shifts are investigated. We show that the discrete orthogonality relations hold for the case-(1) multi-indexed orthogonal polynomials of continuous Hahn, Wilson and Askey-Wilson types, and conjecture their normalization ...
arxiv +1 more source
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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