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BESSELINT is a Matlab program to integrate arbitrary products of Bessel functions over the real halfline. Only Bessel functions of the first kind are currently supported.


Our program was written to work in Matlab 7.0 and Octave 2.1.69. However, we specifically implemented it to be backward compatible with earlier versions of Matlab. We extensively tested our code under

  • Matlab (R2006a) for Linux
  • Matlab (R14) Service Pack 1 for Linux
  • Matlab (R13) for Linux and Windows
  • Matlab (R12.1) for Windows
  • Octave 2.1.69


Once the main reference given below is published, it will be available at the ACM Digital Library and Netlib. In the mean time, you can obtain it by asking one of the authors.


The main reference for this software project.

  1. J. Van Deun and R. Cools. Algorithm 858: Computing infinite range integrals of an arbitrary product of Bessel functions. ACM Trans. Math. Software, Vol. 32(4) pp. 580-596. 2006.

Some implementation issues and related work.

  1. J. Van Deun and R. Cools. Integrating products of Bessel functions using the incomplete gamma function. In T.E. Simos, G. Psihoyios, and Ch. Tsitouras, editors, International Conference on Numerical Analysis and Applied Mathematics 2005, pp. 668-671. Wiley-VCH. 2005.
  2. J. Van Deun and R. Cools. A Matlab implementation of an algorithm for computing integrals of products of Bessel functions. In Second International Congress on Mathematical Software, Lecture Notes in Computer Science, pp. 284-295. Springer, ISBN: 978-3-540-38084-9. 2006.
  3. J. Van Deun and R. Cools. Note on "Electromagnetic Response of a Large Circular Loop Source on a Layered Earth: A New Computation Method". Pure and Applied Geophysics, Vol. 164(5) pp. 1107-1111. 2007.
  4. J. Van Deun and R. Cools. A stable recurrence for the incomplete gamma function with imaginary second argument. Numerische Mathematik, Vol. 104(4) pp. 445-456. 2006.
  5. J. Van Deun and R. Cools. Integrating products of Bessel functions with an additional exponential or rational factor. Computer Physics Communications, Vol. 178(8) pp. 578-590. 2008.