Results 21 to 30 of about 552,136 (253)
Comptes Rendus. MathématiqueWe give a new family of Karhunen-Loève expansions involving Hahn polynomials. This enables us to introduce discrete analogues of Watson statistics, and a test for uniformity on Johnson’s graphs. We use the fact that the zonal spherical functions on these
Pycke, Jean-Renaud
doaj +2 more sources
Hahn polynomials on polyhedra and quantum integrability [PDF]
Advances in Mathematics, 2020 Orthogonal polynomials with respect to the hypergeometric distribution on lattices in polyhedral domains in ${\mathbb R}^d$, which include hexagons in ${\mathbb R}^2$ and truncated tetrahedrons in ${\mathbb R}^3$, are defined and studied. The polynomials are given explicitly in terms of the classical one-dimensional Hahn polynomials.
Plamen Iliev, Yuan Xu
openaire +4 more sources
The Cauchy Operator and the Homogeneous Hahn Polynomials [PDF]
American Journal of Applied Mathematics, 2021 The Cauchy operator plays important roles in the theory of basic hypergeometric series. As some applications, our purpose is mainly to show new proofs of the Mehler’s formula, the Rogers formula and the generating function for the homogeneous Hahn polynomials Φ(α)n(x,y|q)) by making use of the Cauchy operator and its properties.
Xinhao Huang, Zhizheng Zhang, Qiuxia Hu
openaire +3 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
core +5 more sources
Hahn, Jacobi, and Krawtchouk polynomials of several variables
Journal of Approximation Theory, 2014 22 ...
Yuan Xu
openalex +4 more sources
Dual -1 Hahn polynomials and perfect state transfer [PDF]
, 2011 We find all the $XX$ spin chains with perfect state transfer (PST) that are connected with the dual -1 Hahn polynomials $R_n(x; \alpha,\beta,N)$. For $N$ odd we recover a model that had already been identified while for $N$ even, we obtain a new system ...
AKay +11 more
core +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
core +3 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
Two q-Operational Equations and Hahn Polynomials
Complex Analysis and Operator TheoryMotivated 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. As applications, we use the method of $q$-exponential operator to prove the bilinear generating function of ...
Gu, Jing, Yang, DunKun, Bao, Qi
openaire +3 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