# A Matlab Implementation of an Algorithm for Computing Integrals of Products of Bessel Functions

```@inproceedings{Deun2006AMI,
title={A Matlab Implementation of an Algorithm for Computing Integrals of Products of Bessel Functions},
author={J. V. Deun and R. Cools},
booktitle={ICMS},
year={2006}
}```
• Published in ICMS 2006
• Computer Science
We present a Matlab program that computes infinite range integrals of an arbitrary product of Bessel functions of the first kind. The algorithm uses an integral representation of the upper incomplete Gamma function to integrate the tail of the integrand. This paper describes the algorithm and then focuses on some implementation aspects of the Matlab program. Finally we mention a generalisation that incorporates the Laplace transform of a product of Bessel functions.

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#### References

SHOWING 1-10 OF 32 REFERENCES
Evaluating infinite integrals involving products of Bessel functions of arbitrary order
The difficulties involved with evaluating infinite integrals involving products of Bessel functions are considered, and a method for evaluating these integrals is outlined. The method makes use ofExpand
The evaluation of integrals of Bessel functions via G -function identities
A few transformations are presented for reducing certain cases of Meijer's G-function to a G-function of lower order. Their applications to the integration of a product of Bessel functions are given.Expand
On the numerical evaluation of an oscillating infinite series
Abstract An oscillating infinite series involving products of the Bessel function J 0 ( x ) is evaluated. The series is transformed first into the sum of three infinite integrals by using contourExpand
Computing the Incomplete Gamma Function to Arbitrary Precision
It is shown that the incomplete Gamma function Γ (a, z) can be computed to P digits in at most O(P) long multiplications uniformly in z for Re z > 0. Expand
A Treatise on the Theory of Bessel Functions
THE memoir in which Bessel, the astronomer, examined in detail the functions which now bear his name was published in 1824, and was the outcome of his earlier researches concerning the expression ofExpand
An efficient solution of a class of integrals arising in antenna theory
• S. Savov
• Mathematics
• IEEE Antennas and Propagation Magazine
• 2002
A novel analytical solution for a class of power-radiation integrals, arising in antenna theory, is presented. These integrals are then applied to the analysis of circular-loop andExpand
An Efficient Solution of a Class of Integrals Arising in Antenna Theory
• Physics
• 2002
A novel analytical solution for a class of power-radiation integrals, arising in antenna theory, is presented. These integrals are then applied to the analysis of circular-loop andExpand
A stable recurrence for the incomplete gamma function with imaginary second argument
• Mathematics, Computer Science
• Numerische Mathematik
• 2006
This work presents an approach to compute the recurrence relation to full precision, also for small values of the arguments, when the first argument is negative and the second one is purely imaginary. Expand
On an integral related to biaxially anisotropic media
• Mathematics
• 2002
An integral arising in certain studies of theoretical electromagnetics is evaluated and its properties are discussed in some detail. The integral has three integer, two real, and one complexExpand
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)
• Computer Science
• 1965
The handbook of mathematical functions with formulas graphs and mathematical tables national bureau of standards applied mathematics series 55 that we provide for you will be ultimate to giveExpand