@misc{10481/70819,
year = {2021},
month = {8},
url = {http://hdl.handle.net/10481/70819},
abstract = {In this work, the spread of hypergeometric orthogonal polynomials (HOPs) along their
orthogonality interval is examined by means of the main entropy-like measures of their associated
Rakhmanov’s probability density—so, far beyond the standard deviation and its generalizations, the
ordinary moments. The Fisher information, the Rényi and Shannon entropies, and their corresponding
spreading lengths are analytically expressed in terms of the degree and the parameter(s) of the
orthogonality weight function. These entropic quantities are closely related to the gradient functional
(Fisher) and the Lq-norms (Rényi, Shannon) of the polynomials. In addition, the degree asymptotics
for these entropy-like functionals of the three canonical families of HPOs (i.e., Hermite, Laguerre,
and Jacobi polynomials) are given and briefly discussed. Finally, a number of open related issues are
identified whose solutions are both physico-mathematically and computationally relevant.},
organization = {Agencia Estatal de Investigacion (Spain)},
organization = {European Commission	PID2020-113390GB-I00},
publisher = {MDPI},
keywords = {Special functions},
keywords = {Classical orthogonal polynomials},
keywords = {Entropy-like measures},
keywords = {Asymptotics},
title = {Entropy-Like Properties and L-q-Norms of Hypergeometric Orthogonal Polynomials: Degree Asymptotics},
doi = {10.3390/sym13081416},
author = {Sánchez-Dehesa Moreno-Cid, Jesús},
}