A Bessel type orthogonal polynomial system

Polynomial Approximations to Bessel Functions

A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order have similar accuracies.

Evaluation of integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example

Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a new method for evaluating integrals that include orthogonal polynomials. The method is illustrated by obtaining the following integral result that involves the Bessel function and associated Laguerre polynomial: integral(infinity)(0) x(v)e(-x/2) J(v)(mu x)L-n(2v)(x)dx = 2(v)Ga...

A Robust Nonlinear System Identification Algorithm using Orthogonal Polynomial Network

Multiple orthogonal polynomial ensembles

Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we introduce the notion of a multiple orthogonal polynomial ensemble (MOP ensemble) and derive some of their basic properties. It is shown that Angelesco and Niki...

Orthogonal Polynomials and Polynomial Approximations

3.1.1. Existence and uniqueness. Our immediate goal is to establish the existence of a sequence of orthogonal polynomials. Although we could, in principle, determine the coefficients a j of pn in the natural basis by using the orthogonality conditions (3.1.2), it is computationally advantageous to express pn in terms of lower-order orthogonal polynomials. Let us denote Pn := span { 1, x, x, · ·...