Evaluating infinite integrals involving Bessel functions of arbitrary order

[摘要] The evaluation of integrals of the form I-n = integral(0)(infinity)f(x)J(n)(x)dx is considered. In the past, the method of dividing an oscillatory integral at its zeros, forming a sequence of partial sums, and using extrapolation to accelerate convergence has been found to be the most efficient technique available where the oscillation is due to a trigonometric function or a Bessel function of order n = 0, 1. Here, we compare various extrapolation techniques as well as choices of endpoints in dividing the integral, and establish the most efficient method for evaluating infinite integrals involving Bessel functions of any order n, not just zero or one. We also outline a simple but very effective technique for calculating Bessel function zeros.

[发布日期] 1995-12-20

[关键词] quadrature;infinite integration;Bessel functions;Bessel zeros;E-algorithm;mW transform