Information-Theoretic-Based Spreading Measures of Orthogonal Polynomials

Direct spreading measures of Laguerre polynomials

The direct spreading measures of the Laguerre polynomials L (α) n (x), which quantify the distribution of its Rakhmanov probability density ρn,α(x) = 1 dn xαe−x [ L (α) n (x) ]2 along the positive real line in various complementary and qualitatively different ways, are investigated. These measures include the familiar rootmean-square or standard deviation and the information-theoretic lengths o...

On Generating Orthogonal Polynomials for Discrete Measures

Fisher information of orthogonal polynomials I

Following the lead of J. Dehesa and his collaborators, we compute the Fisher information of the Meixner-Pollaczek, Meixner, Krawtchouk and Charlier polynomials.

Determining The Specificity Of Terms Based On Information Theoretic Measures

This paper introduces new specificity determining methods for terms based on information theoretic measures. The specificity of terms represents the quantity of domain specific information that is contained in the terms. Compositional and contextual information of terms are used in proposed methods. As the methods don’t rely on domain dependent information, they can be applied to other domains ...

Monotonicity of the zeros of orthogonal polynomials through related measures

Relation between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), is well known. We use this relation to study the monotonicity properties of the zeros of generalized orthogonal polynomials. As examples, the Jacobi, Laguerre and Charlier polynomials are considered.  2005 Elsevier Inc. All...