New method for evaluating integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example

Details New method for evaluating integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example New method for evaluating integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example

2005-12-04

arxiv.org/abs/math-ph/0512010v1

Appl. Math. Lett. 20.1 (2007) 38-42

Physics

Mathematical Physics

Abstract does not display the integral result, which is in an image format shown in the Abstract on the manuscript

Scientific paper

Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a method for evaluating new integrals. The method is illustrated by obtaining a closed-form expression for the value of an integral that involves the Bessel function and associated Laguerre polynomial. The result, which is given by Eq. (19) in the text, is written in terms of the Gegenbauer (ultra-spherical) polynomial.

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