Results 11 to 20 of about 552,136 (253)
Asymptotic approximations of the continuous Hahn polynomials and their zeros [PDF]
Journal of Approximation Theory, 2019 Asymptotic approximations for the continuous Hahn polynomials and their zeros as the degree grows to infinity are established via their three-term recurrence relation. The methods are based on the uniform asymptotic expansions for difference equations developed by Wang and Wong (\textit{Numer.
Lihua Cao, Yutian Li, Yu Lin
semanticscholar +6 more sources
Fast and stable computation of higher-order Hahn polynomials and Hahn moment invariants for signal and image analysis. [PDF]
Multimed Tools Appl, 2021 This article presents, on the one hand, new algorithms for the fast and stable computation of discrete orthogonal Hahn polynomials of high order (HPs) based on the elimination of all gamma and factorial functions that cause the numerical fluctuations of ...
Daoui A +3 more
europepmc +2 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 +2 more sources
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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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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Hahn polynomials for hypergeometric distribution [PDF]
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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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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Bispectrality of the Complementary Bannai-Ito Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 A one-parameter family of operators that have the complementary Bannai-Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai-Ito polynomials and also correspond to a q→−1 limit of the Askey-Wilson ...
Vincent X. Genest +2 more
doaj +5 more sources
On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Tom H. Koornwinder
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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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