Cramer-Rao information plane of orthogonal hypergeometric polynomials

  • Authors:

  • J. S. Dehesa;P. Sánchez-Moreno;R. J. Yáñez

  • Affiliations:

  • Departamento de Física Moderna, Universidad de Granada, Granada, Spain and Instituto "Carlos I" de Física Teórica y Computacional, Universidad de Granada, Granada, Spain;Departamento de Física Moderna, Universidad de Granada, Granada, Spain and Instituto "Carlos I" de Física Teórica y Computacional, Universidad de Granada, Granada, Spain;Instituto "Carlos I" de Física Teórica y Computacional, Universidad de Granada, Granada, Spain and Departamento de Matemática Aplicada, Universidad de Granada, Granada, Spain

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2006

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Abstract

The classical hypergeometric polynomials {pn(x)}n=0∞, which are orthogonal with respect to a weight function ω(x) defined on a real interval, are analyzed in the Cramer-Rao information plane, that is the plane defined by both Fisher information and variance of the probability density ρn(x) = pn(x)2ω(x). The Rakhmanov density ρn(x) of these polynomials, which describes the probability density of the quantum states for various physical prototypes in an exact manner and for numerous physical systems to a very good approximation, is discussed in detail.