Information entropy of Gegenbauer polynomials
نویسندگان
چکیده
The information entropy of Gegenbauer polynomials is relevant since this is related to the angular part of the information entropies of certain quantum mechanical systems such as the harmonic oscillator and the hydrogen atom in D dimensions. We give an effective method to compute the entropy for Gegenbauer polynomials with an integer parameter and obtain the first few terms in the asymptotic expansion as the degree of the polynomial tends to infinity.
منابع مشابه
Entropic Integrals of Hyperspherical Harmonics and Spatial Entropy of D-Dimensional Central Potentials
The information entropy of a single particle in a quantum-mechanicalD-dimensional central potential is separated in two parts. One depends only on the specific form of the potential (radial entropy) and the other depends on the angular distribution (spatial entropy). The latter is given by an entropic-like integral of the hyperspherical harmonics, which is expressed in terms of the entropy of t...
متن کاملInformation entropy of Gegenbauer polynomials and Gaussian quadrature
In a recent paper (Buyarov V S, López-Artés P, Martı́nez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549–60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C n (x) in the case when λ = l ∈ N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary...
متن کاملComputation of the Entropy of Polynomials Orthogonal on an Interval
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that 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...
متن کاملA new Extension of Gegenbauer Matrix Polynomials and Their Properties
The aim of this paper is to define and study of the Gegenbauer matrix polynomials of two variables. An explicit representation, a three-term matrix recurrence relations, differential recurrence relations and hypergeometric matrix representation for the Gegenbauer matrix polynomials of two variables are given. The Gegenbauer matrix polynomials are solutions of the matrix differential equations a...
متن کاملComputing with Expansions in Gegenbauer Polynomials
In this work, we develop fast algorithms for computations involving finite expansions in Gegenbauer polynomials. We describe a method to convert a linear combination of Gegenbauer polynomials up to degree n into a representation in a different family of Gegenbauer polynomials with generally O(n log(1/ε)) arithmetic operations where ε is a prescribed accuracy. Special cases where source or targe...
متن کامل