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

Joris Van Deun, Ronald Cools

Code and Data 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.

Article

Joris Van Deun, Ronald Cools, et al. " Algorithm 858: Computing infinite range integrals of an arbitrary product of Bessel functions." ACM Transactions on Mathematical Software.     doi:10.1145/1186785.1186790. Retrieved 06/24/2019 from researchcompendia.org/compendia/2013.300/

Compendium Type: Published Papers
Primary Research Field: Computer and Information Sciences
Secondary Research Field: Mathematics
Content License: Public Domain Mark
Code License: MIT License

Page Owner

jenn.seiler@gmail.com

created 12/12/2013

modified 01/16/2014

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