We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a semiclassical Laguerre weight and classical solutions of the fourth Painlevé equation. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of parabolic cylinder functions which arise in the description of special function solutions of the fo...

Kleinewillinghöfer classified Laguerre planes with respect to central automorphisms and obtained a multitude of types. In this paper we investigate the Kleinewillinghöfer types of finite Laguerre planes with respect to homotheties and deal with some of the larger types.

We present some geometric relationships between the ordinary Voronoi diagram, and the Voronoi diagram in the Laguerre geometry. We derive from these properties an algorithm for the conversion of ordinary Voronoi diagrams into Voronoi diagrams in the Laguerre geometry.

New inequalities are investigated for real entire functions in the Laguerre-Pólya class. These are generalizations of the classical Turán and Laguerre inequalities. They provide necessary conditions for certain real entire functions to have only real zeros.

In this paper we prove Riesz transform characterizations for Hardy spaces associated with certain systems of Laguerre functions.

A new type of biosensor, based on hippocampal slices cultured on multielectrode arrays, and using nonlinear systems analysis for the detection and classification of agents interfering with cognitive function is described. A new method for calculating first and second order kernel was applied for impulse input-spike output datasets and results are presented to show the reliability of the estimat...

Let fSng denote the sequence of polynomials orthogonal with respect to the Sobolev inner product

In this paper, unstructured system identification algorithm based on orthonormal Laguerre functions is combined with predictive functional control such that similar classical PI controller is constructed. Lack of mathematical model and initial information about process is not a restriction for mentioned algorithm and unstructured system identification based on Laguerre functions can overcome th...

We show that a certain generalized beta function B(x; y; b) which reduces to Euler’s beta functions B(x; y) when its variable b vanishes and preserves symmetry in its parameters may be represented in terms of a nite number of well known higher transcendental functions except (possibly) in the case when one of its parameters is an integer and the other is not. In the latter case B(x; y; b) may b...