Results 11 to 20 of about 634 (218)
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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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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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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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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Hahn polynomials and the Burnside process [PDF]
The Ramanujan Journal, 2021 We study a natural Markov chain on $\{0,1,\cdots,n\}$ with eigenvectors the Hahn polynomials. This explicit diagonalization makes it possible to get sharp rates of convergence to stationarity. The process, the Burnside process, is a special case of the celebrated `Swendsen-Wang' or `data augmentation' algorithm.
Persi Diaconis, Chenyang Zhong
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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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Hahn, Jacobi, and Krawtchouk polynomials of several variables
Journal of Approximation Theory, 2014 22 ...
Yuan Xu
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On Jacobi and continuous Hahn polynomials [PDF]
Proceedings of the American Mathematical Society, 1996 The inter-relation between the Jacobi polynomials and the continuous Hahn polynomials via the Fourier transform is exploited to deduce the orthogonality relation of the latter from that of the former and the use of Parseval's relation. This is an additional independent case of the proof of this important relation whereby the general theory of special ...
H.T. Koelink, H.T. Koelink
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Hahn polynomials for hypergeometric distribution
Advances in Applied Mathematics, 2022 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 ...
Iliev, Plamen, Xu, Yuan
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On difference operators for symmetric Krall-Hahn polynomials [PDF]
Integral Transforms and Special Functions, 2018 18 ...
Antonio J. Durán +1 more
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