Fisher information of orthogonal hypergeometric polynomials
The authors explicitly calculate the Fisher information of the continuous orthogonal polynomials of hypergeometric type directly in terms of the coefficients of the second-order differential equation that they satisfy and the connection coefficients between the members of these polynomial families. This leads to the analytic expression of the Fisher transformation for the classical polynomials of Hermite, Laugerre and Jacobi, as a function of the degree and the parameters of the polynomials. Contrary to the Shannon entropy of \textit{J. S. Dehesa, A. Martínez-Finkelshtein} and \textit{J. Sánchez-Ruiz} [J. Comput. Appl. Math. 133, 23--46 (2001; Zbl 1008.81014)], the Fisher information of these polynomials can be explicitly given in closed form. The asymptotic behaviour of the Fisher information with respect to the degree of the polynomials is linear for the Hermite and Laguerre cases, and cubic for the Jacobi case.
scientific article; zbMATH DE number 2184011
scientific article