Back to Search
Start Over
Cramer–Rao information plane of orthogonal hypergeometric polynomials
- Source :
- Journal of Computational and Applied Mathematics. 186(2):523-541
- Publication Year :
- 2006
- Publisher :
- Elsevier BV, 2006.
-
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.
- 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
Subjects
Details
- ISSN :
- 03770427
- Volume :
- 186
- Issue :
- 2
- Database :
- OpenAIRE
- Journal :
- Journal of Computational and Applied Mathematics
- Accession number :
- edsair.doi.dedup.....dc2b01138a27ef3402826e9097389c0d
- Full Text :
- https://doi.org/10.1016/j.cam.2005.03.025