1. Cramer–Rao information plane of orthogonal hypergeometric polynomials
- Author
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Rafael J. Yáñez, Pablo Sánchez-Moreno, and Jesús S. Dehesa
- Subjects
Weight function ,Pure mathematics ,Information theory ,Fisher information ,Cramer–Rao inequalities ,Plane (geometry) ,Applied Mathematics ,Classical orthogonal polynomials ,Probability density function ,Variance ,Combinatorics ,symbols.namesake ,Computational Mathematics ,Special functions ,Orthogonal polynomials ,symbols ,Jacobi polynomials ,Cramer–Rao information plane ,Mathematics - 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.
- Published
- 2006
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