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Reports on Mathematical Physics, Volume 82, Issue 3, December
2018, Pages 285-301, 2017 Using a formulation of quantum mechanics based on the theory of orthogonal polynomials, we introduce a four-parameter system associated with the Hahn and continuous Hahn polynomials. The continuum energy scattering states are written in terms of the continuous Hahn polynomial whose asymptotics give the scattering amplitude and phase shift. On the other
A. D. Alhaidari, Yutian Li
arxiv +6 more sources
Doubling (Dual) Hahn Polynomials: Classification and Applications [PDF]
SIGMA 12 (2016), 003, 27 pages, 2015 We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest comes from an example appearing in a finite oscillator model [Jafarov E.I., Stoilova N.I., Van der Jeugt J., J. Phys. A: Math. Theor.
R. Oste, J. Jeugt
arxiv +9 more sources
Performance enhancement of high order Hahn polynomials using multithreading. [PDF]
PLoS ONE, 2023 Orthogonal polynomials and their moments have significant role in image processing and computer vision field. One of the polynomials is discrete Hahn polynomials (DHaPs), which are used for compression, and feature extraction.
Basheera M Mahmmod +5 more
doaj +3 more sources
Fast Computation of Hahn Polynomials for High Order Moments [PDF]
IEEE Access, 2022 Discrete Hahn polynomials (DHPs) and their moments are considered to be one of the efficient orthogonal moments and they are applied in various scientific areas such as image processing and feature extraction.
Basheera M. Mahmmod +3 more
doaj +4 more sources
Hahn polynomials for hypergeometric distribution [PDF]
Adv. in Appl. Math. 139 (2022), Paper No. 102364, 34pp, 2020 Orthogonal polynomials for the multivariate hypergeometric distribution are defined on lattices in polyhedral domains in $\RR^d$. Their structures are studied through a detailed analysis of classical Hahn polynomials with negative integer parameters. Factorization of the Hahn polynomials is explored and used to explain the relation between the index ...
P. Iliev, Yuan Xu
arxiv +5 more sources
Fourier Transform of the Orthogonal Polynomials on the Unit Ball and Continuous Hahn Polynomials [PDF]
Axioms, 2022 Some systems of univariate orthogonal polynomials can be mapped into other families by the Fourier transform. The most-studied example is related to the Hermite functions, which are eigenfunctions of the Fourier transform.
Esra Güldoğan Lekesiz +2 more
doaj +5 more sources
A Discrete Cramér–Von Mises Statistic Related to Hahn Polynomials with Application to Goodness-of-Fit Testing for Hypergeometric Distributions [PDF]
AxiomsWe give the Karhunen–Loève expansion of the covariance function of a family of discrete weighted Brownian bridges, appearing as discrete analogues of continuous Gaussian processes related to Cramér –von Mises and Anderson–Darling statistics. This analogy
Jean-Renaud Pycke
doaj +3 more sources
A Spectral Method Based on Hahn Polynomials for Numerical Solution of Fractional Integro-Differential Equations with Weakly Singular Kernel [PDF]
پژوهشهای ریاضی, 2020 Introduction Despite wide applications of constant order fractional derivatives, some systems require the use of derivatives whose order changes with respect to other parameters.
Farideh Salehi +2 more
doaj +3 more sources
On difference operators for symmetric Krall-Hahn polynomials [PDF]
Integral Transforms and Special Functions, 2018 The problem of finding measures whose orthogonal polynomials are also eigenfunctions of higher-order difference operators have been recently solved by multiplying the classical discrete measures by suitable polynomials. This problem was raised by Richard
A. J. Durán, Manuel D. de la Iglesia
semanticscholar +7 more sources
The multivariate Hahn polynomials and the singular oscillator [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 Karlin and McGregorʼs d-variable Hahn polynomials are shown to arise in the ( d + 1 ) ?> -dimensional singular oscillator model as the overlap coefficients between bases associated with the separation of variables in Cartesian and hyperspherical ...
Vincent X. Genest, L. Vinet
semanticscholar +6 more sources