Results 1 to 10 of about 619 (209)
An Exactly Solvable Spin Chain Related to Hahn Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter α and depends on the parity of the chain site.
Neli I. Stoilova, Joris Van der Jeugt
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On the Orthogonality of q-Classical Polynomials of the Hahn Class [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial solutions of the q-hypergeometric difference equation on a q-linear lattice by means of a qualitative analysis of the q-Pearson ...
Renato Álvarez-Nodarse +2 more
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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
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GLOBAL ASYMPTOTICS OF THE HAHN POLYNOMIALS [PDF]
Analysis and Applications, 2012 In this paper, we study the asymptotics of the Hahn polynomials Qn(x; α, β, N) as the degree n grows to infinity, when the parameters α and β are fixed and the ratio of n/N = c is a constant in the interval (0, 1). Uniform asymptotic formulas in terms of Airy functions and elementary functions are obtained for z in three overlapping regions, which ...
Yu Lin, R. Wong
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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
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Constructing Krall-Hahn orthogonal polynomials
Journal of Mathematical Analysis and Applications, 2014 Given a sequence of polynomials $(p_n)_n$, an algebra of operators $\mathcal A$ acting in the linear space of polynomials and an operator $D_p\in \mathcal A$ with $D_p(p_n)= _np_n$, where $ _n$ is any arbitrary eigenvalue, we construct a new sequence of polynomials $(q_n)_n$ by considering a linear combination of $m+1$ consecutive $p_n$: $q_n=p_n ...
Antonio J. Durán +1 more
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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
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Quantum Systems Associated with the Hahn and Continuous Hahn Polynomials [PDF]
Reports on Mathematical Physics, 2018 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, Y.-T. Li
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Multivariable q-Hahn polynomials as coupling coefficients for quantum algebra representations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 We study coupling coefficients for a multiple tensor product of highest weight representations of the SU(1,1) quantum group. These are multivariable generalizations of the q-Hahn polynomials.
Hjalmar Rosengren
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The multivariate Hahn polynomials and the singular oscillator [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 Karlin and McGregor's d-variable Hahn polynomials are shown to arise in the (d+1)-dimensional singular oscillator model as the overlap coefficients between bases associated to the separation of variables in Cartesian and hyperspherical coordinates. These polynomials in d discrete variables depend on d+1 real parameters and are orthogonal with respect ...
Vincent X. Genest, Luc Vinet
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