Fisher information of orthogonal hypergeometric polynomials

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Show simple item record Sánchez-Ruiz, Jorge Sánchez Dehesa, Jesús 2010-01-22T13:35:44Z 2010-01-22T13:35:44Z 2005-10-01
dc.identifier.bibliographicCitation Journal of Computational and Applied Mathematics, 2005, vol. 182, n. 1, p. 150-164
dc.identifier.issn 0377-0427
dc.description.abstract The probability densities of the position and momentum of many quantum systems have the form $\rho(x)\propto p_n\sp 2(x)\omega(x)$, where $\{p_n(x)\}$ denotes a sequence of hypergeometric-type polynomials orthogonal with respect to the weight function $\omega(x)$. Here we derive an explicit expression for the Fisher information $I=\int {\rm d}x[\rho'(x)]\sp 2/\rho(x)$ corresponding to this kind of distribution, in terms of the coefficients of the second-order differential equation satisfied by the polynomials $p_n(x)$. We work out in detail the particular cases of the classical Hermite, Laguerre and Jacobi polynomials, for which we find the value of Fisher information in closed analytical form and study its asymptotic behaviour in the large-$n$ limit.
dc.format.mimetype text/html
dc.language.iso eng
dc.publisher Elsevier
dc.subject.other Classical orthogonal polynomials
dc.subject.other Fisher information
dc.subject.other Second-order differential equations
dc.subject.other Probability measures
dc.title Fisher information of orthogonal hypergeometric polynomials
dc.type article PeerReviewed
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/
dc.rights.accessRights openAccess
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