From continuous to discrete: weak limit of normalized Askey–Wilson measure

DOI10.1007/S11139-023-00820-3WikidataQ129931042 ScholiaQ129931042MaRDI QIDQ6500205

Xiang-Sheng Wang, Mourad E. H. Ismail, Dan Dai

Publication date: 10 May 2024

Published in: The Ramanujan Journal (Search for Journal in Brave)

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Other functions coming from differential, difference and integral equations (33E30) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the Askey scheme
Q-Gaussian distributions: simplifications and simulations
$-1$ Krall-Jacobi polynomials
Zeros and orthogonality of the Askey-Wilson polynomials for $q$ a root of unity
CMV matrices and little and big $-1$ Jacobi polynomials
A limit $q=-1$ for the big $q$-Jacobi polynomials
Can thegeneralsolution of the second-order ODE characterizing Jacobi polynomials bepolynomial?
Diophantine properties of the zeros of certain Laguerre and para-Jacobi polynomials
Diophantine properties of orthogonal polynomials and rational functions
Polynomials Defined by Three-Term Recursion Relations and Satisfying a Second Recursion Relation: Connection with Discrete Integrability, Remarkable (Often Diophantine) Factorizations
Sieved Ultraspherical Polynomials
Recurrence relations, continued fractions, and orthogonal polynomials
Proof of certain Diophantine conjectures and identification of remarkable classes of orthogonal polynomials
Hypergeometric origins of Diophantine properties associated with the Askey scheme
Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
Convolutions of Orthonormal Polynomials
q-Hermite Polynomials, Biorthogonal Rational Functions, and q-Beta Integrals
The Moment Problem
Isochronous Systems
Tridiagonal matrices, orthogonal polynomials and Diophantine relations: II
Tridiagonal matrices, orthogonal polynomials and Diophantine relations: I
Convergence of spectral likelihood approximation based on q-Hermite polynomials for Bayesian inverse problems

This page was built for publication: From continuous to discrete: weak limit of normalized Askey–Wilson measure