# Fisher information of orthogonal hypergeometric polynomials

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 dc.contributor.author Sánchez-Ruiz, Jorge dc.contributor.author Sánchez Dehesa, Jesús dc.date.accessioned 2010-01-22T13:35:44Z dc.date.available 2010-01-22T13:35:44Z dc.date.issued 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.identifier.uri http://hdl.handle.net/10016/6586 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 dc.type.review PeerReviewed dc.description.status Publicado dc.relation.publisherversion http://dx.doi.org/10.1016/j.cam.2004.09.062 dc.subject.eciencia Matemáticas dc.identifier.doi 10.1016/j.cam.2004.09.062 dc.rights.accessRights openAccess
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