On difference operators for symmetric Krall-Hahn polynomials [PDF]
Integral Transforms and Special Functions, 2018 18 ...
Antonio J. Durán +1 more
openalex +5 more sources
Hahn, Jacobi, and Krawtchouk polynomials of several variables
Journal of Approximation Theory, 2014 22 ...
Yuan Xu
openalex +4 more sources
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
openalex +4 more sources
Fourier Transform of the Orthogonal Polynomials on the Unit Ball and Continuous Hahn Polynomials
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 +4 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 +2 more sources
The Weyl algebra, spherical harmonics, and Hahn polynomials [PDF]
Banach Center Publications, 2002 13 pages, uses bcp01e ...
Ewa Gnatowska, Aleksander Strasburger
openalex +4 more sources
The Hahn polynomials in the nonrelativistic and relativistic Coulomb problems [PDF]
Journal of Mathematical Physics, 2008 We derive closed formulas for mean values of all powers of r in nonrelativistic and relativistic Coulomb problems in terms of the Hahn and Chebyshev polynomials of a discrete variable. A short review on special functions and solution of the Coulomb problems in quantum mechanics is given.
Sergeĭ K. Suslov, Benjamin Trey
openalex +4 more sources
An Introduction to the q-Laguerre-Hahn Orthogonal q-Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2011 Orthogonal q-polynomials associated with q-Laguerre-Hahn form will be studied as a generalization of the q-semiclassical forms via a suitable q-difference equation. The concept of class and a criterion to determinate it will be given.
Abdallah Ghressi +2 more
doaj +2 more sources
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
openaire +3 more sources
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
openaire +2 more sources