Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6586

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 Title: Fisher information of orthogonal hypergeometric polynomials Author(s): Sánchez-Ruiz, JorgeSánchez Dehesa, Jesús Publisher: Elsevier Issued date: 1-Oct-2005 Citation: Journal of Computational and Applied Mathematics, 2005, vol. 182, n. 1, p. 150-164 URI: http://hdl.handle.net/10016/6586 ISSN: 0377-0427 DOI: 10.1016/j.cam.2004.09.062 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. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1016/j.cam.2004.09.062 Keywords: Classical orthogonal polynomialsFisher informationSecond-order differential equationsProbability measures Appears in Collections: DM - GAMA - Artículos de Revistas