Entropic integrals of orthogonal hypergeometric polynomials with general supports
type: Item
instance of: scholarly article
title: Entropic integrals of orthogonal hypergeometric polynomials with general supports
zbMATH Open document ID: 0953.33004
DOI: 10.1016/S0377-0427(00)00296-X
author: Jorge Sánchez-Ruiz
author: Jesús S. Dehesa
published in: Journal of Computational and Applied Mathematics
publication date: 2001-01-30T00:00:00Z
review text: Two integrals arise in the calculation of the Boltzman-Shannon entropy of probability measures associated with continuous hypergeometric polynomials \(\{p_n(x)\}\) orthogonal with respect to a general weight function \(\omega(x)\) on an interval \(J\). The authors focus on the calculation of the integral \(I_n=-\int_J p^2_np^2_n(x) \omega(x) \ln\omega (x)dx\) over intervals with compact and noncompact support. They derive a recursion relation and closed analytic expressions for a family of integrals that includes \(I_n\). Their formulae only involve the coefficients of the differential equation satisfied by the polynomials \(p_n(x)\). The formulae are applied to evaluate \(I_n\) for the Hermite, Laguerre and Jacobi polynomials.
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1472347
zbMATH Keywords: entropic integrals
zbMATH Keywords: orthogonal hypergeometric polynomials
zbMATH Keywords: Hermite polynomials
zbMATH Keywords: Laguerre polynomials
zbMATH Keywords: Jacobi polynomials
Wikidata QID: Q58363401
reviewed by: Peter A. McCoy
MaRDI profile type: Publication
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full work available at URL: s0377-0427(00)00296-x
OpenAlex ID: W2131966285
description: scientific article; zbMATH DE number 1472347