Fisher information of orthogonal hypergeometric polynomials
type: Item
instance of: scholarly article
title: Fisher information of orthogonal hypergeometric polynomials
zbMATH Open document ID: 1081.33017
author: Jorge Sánchez-Ruiz
author: Jesús S. Dehesa
published in: Journal of Computational and Applied Mathematics
publication date: 2005-06-30T00:00:00Z
review text: The authors explicitly calculate the Fisher information of the continuous orthogonal polynomials of hypergeometric type directly in terms of the coefficients of the second-order differential equation that they satisfy and the connection coefficients between the members of these polynomial families. This leads to the analytic expression of the Fisher transformation for the classical polynomials of Hermite, Laugerre and Jacobi, as a function of the degree and the parameters of the polynomials. Contrary to the Shannon entropy of \textit{J. S. Dehesa, A. Martínez-Finkelshtein} and \textit{J. Sánchez-Ruiz} [J. Comput. Appl. Math. 133, 23--46 (2001; Zbl 1008.81014)], the Fisher information of these polynomials can be explicitly given in closed form. The asymptotic behaviour of the Fisher information with respect to the degree of the polynomials is linear for the Hermite and Laguerre cases, and cubic for the Jacobi case.
reviewed by: P. R. Parthasarathy
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 2184011
zbMATH Keywords: Fisher information
zbMATH Keywords: classical orthogonal polynomials
zbMATH Keywords: probability measures
MaRDI profile type: Publication
full work available at URL: j.cam.2004.09.062
OpenAlex ID: W2112134082
Wikidata QID: Q58363308
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DOI: 10.1016/J.CAM.2004.09.062
description: scientific article; zbMATH DE number 2184011