Computation of the Entropy of Polynomials Orthogonal on an Interval

Authors:
V. Buyarov;J. S. Dehesa
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2005

Citing 0
Cited 9

Information measures of hydrogenic systems, Laguerre polynomials and spherical harmonics

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Cramer-Rao information plane of orthogonal hypergeometric polynomials

Journal of Computational and Applied Mathematics
Shannon entropy of symmetric Pollaczek polynomials

Journal of Approximation Theory
Parameter-based Fisher's information of orthogonal polynomials

Journal of Computational and Applied Mathematics
Asymptotics of orthogonal polynomial's entropy

Journal of Computational and Applied Mathematics
Spreading lengths of Hermite polynomials

Journal of Computational and Applied Mathematics
Information measures of hydrogenic systems, Laguerre polynomials and spherical harmonics

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Cramer-Rao information plane of orthogonal hypergeometric polynomials

Journal of Computational and Applied Mathematics
Direct spreading measures of Laguerre polynomials

Journal of Computational and Applied Mathematics

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Abstract

We give an effective method for computing the entropy for polynomials orthogonal on a segment of the real axis, which uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on a series expression for the mutual energy of two probability measures naturally connected with the polynomials. The particular case of Gegenbauer polynomials is analyzed in detail. These results are applied also to the computation of the entropy of spherical harmonics, important for the study of entropic uncertainty relations as well as the spatial complexity of physical systems in central potentials.