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Manuscript Title: Automatic computation of Bessel function integrals.
Authors: R. Piessens
Program title: HANKEL
Catalogue identifier: AART_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 25(1982)289
Programming language: Fortran.
Computer: IBM 1033.
Operating system: OS/360.
RAM: 9K words
Word size: 32
Keywords: General purpose, Bessel function, Integral over an Infinite interval, Hankel transform, Transform fourier, Atomatic Numerical integration.
Classification: 4.7.

Nature of problem:
Integrals over an infinite interval, involving Bessel functions, occur in many physical applications, especially as Hankel transforms in the solution of certain mixed boundary value problems. In many cases, these integrals cannot be computed analytically and must be evaluated numerically.

Solution method:
Using new approximations for the Bessel functions of the first kind Jv(x), 0<=v<=10, integrals involving Bessel functions can be written as the sum of an integral over a finite interval and of a Fourier-sine and Fourier-cosine transform. For the computation of these three integrals, a lot of methods are available in the literature.

Just as for other numerical integration routines, it is impossible to delineate the class of functions for which this algorithm is accurate, efficient and reliable. However, extensive testing has shown that it works very well for most Bessel function integrals arising in practical problem, if the Bessel function is the only oscillating factor of the integrand.

Running time:
The computation of the 99 integrals in the test run took 7.48 s on the IBM 3033 (including the time required for the computation of the exact values of these integrals).