Quasi-exactly solvable problems and the dual (q-)Hahn polynomials [PDF]
, 1999 A second-order differential (q-difference) eigenvalue equation is constructed whose solutions are generating functions of the dual (q-)Hahn polynomials. The fact is noticed that these generating functions are reduced to the (little q-)Jacobi polynomials,
Granovskii Ya. I. +6 more
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Hahn, Jacobi, and Krawtchouck polynomials of several variables [PDF]
arXiv, 2013 Hahn polynomials of several variables can be defined by using the Jacobi polynomials on the simplex as a generating function. Starting from this connection, a number of properties for these two families of orthogonal polynomials are derived. It is shown that the Hahn polynomials appear as connecting coefficients between several families of orthogonal ...
Yuan Xu
arxiv +3 more sources
Constructing Krall-Hahn orthogonal polynomials [PDF]
, 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 $D_p(p_n)=\theta_np_n$, where $\theta_n$ is any arbitrary eigenvalue, we construct a new ...
Antonio J. Durán +3 more
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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 ...
Iliev, Plamen, Xu, Yuan
core +2 more sources
Two $q$-operational equations and Hahn polynomials [PDF]
arXiv, 2022 Motivated by Liu's recent work in \cite{Liu2022}. We shall reveal the essential feature of Hahn polynomials by presenting two new $q$-exponential operators. These lead us to use a systematic method to study identities involving Hahn polynomials.
Bao, Qi, Gu, Jing, Yang, DunKun
core +1 more source
The multivariate Hahn polynomials and the singular oscillator [PDF]
, 2015 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
Genest, Vincent X., Vinet, Luc
core +3 more sources
Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function [PDF]
arXiv, 1995 Laurent polynomials related to the Hahn-Exton $q$-Bessel function, which are $q$-analogues of the Lommel polynomials, have been introduced by Koelink and Swarttouw.
Koelink, Erik, Van Assche, Walter
core +4 more sources
A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials [PDF]
, 2009 A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials ...
Abramowitz M. +10 more
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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
Dual -1 Hahn polynomials: "classical" polynomials beyond the Leonard duality [PDF]
, 2011 We introduce the -1 dual Hahn polynomials through an appropriate $q \to -1$ limit of the dual q-Hahn polynomials. These polynomials are orthogonal on a finite set of discrete points on the real axis, but in contrast to the classical orthogonal ...
Tsujimoto, Satoshi +2 more
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