Algorithm 858: Computing infinite range integrals of an arbitrary product of Bessel functions

Authors:
Joris Van Deun;Ronald Cools
Affiliations:
Katholieke Universiteit Leuven, Heverlee, Belgium;Katholieke Universiteit Leuven, Heverlee, Belgium
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2006

Citing 5
Cited 2

Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability

Journal of Computational and Applied Mathematics - Numerical Quadrature
On the numerical evaluation of an oscillating infinite series

Journal of Computational and Applied Mathematics
Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order

ACM Transactions on Mathematical Software (TOMS)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Computing the incomplete Gamma function to arbitrary precision

ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI

A matlab implementation of an algorithm for computing integrals of products of bessel functions

ICMS'06 Proceedings of the Second international conference on Mathematical Software
Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions

ACM Transactions on Mathematical Software (TOMS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present an algorithm to compute integrals of the form ∫∞0 xm ∏ki = 1Jνi(aix)dx with Jνi(x) the Bessel function of the first kind and (real) order νi. The parameter m is a real number such that ∑i νi + m −1 and the coefficients ai are strictly positive real numbers. The main ingredients in this algorithm are the well-known asymptotic expansion for Jνi(x) and the observation that the infinite part of the integral can be approximated using the incomplete Gamma function Γ(a,z). Accurate error estimates are included in the algorithm, which is implemented as a MATLAB program.