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Manuscript Title: The Bessel functions J0 and J1 of complex argument.
Authors: R.W.B. Ardill, K.J.M. Moriarty
Program title: BESSEL
Catalogue identifier: ACWZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 13(1977)17
Programming language: Fortran.
Computer: CDC 6600 AND CDC 7600.
Operating system: CDC SCOPE.
RAM: 14K words
Word size: 60
Keywords: General purpose, Expansion, Representation, Eikonal, Impact parameter, Helicity, Partial wave, Bessel function, Complex function.
Classification: 4.7.

Nature of problem:
The Bessel function appears in a wide range of physical applications. The package Bessel contains complex function routines to calculate J0(z) and J1(z) for complex z. Bessel functions of higher order, Jn(z) can be generated by resorting to recurrence relations for n being less than or equal to (z).

The polynomial approximations are designed for |z| <= 10. The program will return results for Jo(z) and J1(z) for all values of |z| up to machine overflow. For |z| <= 10, the maximum absolute error is less than 0.00046, whereas for |z| > 10, the results diverge quite rapidly from their actual values. The accuracy for |z| <= 10 is sufficient for most physical applications, and the polynomial approximations provide a quicker calculation of Bessel functions than the use of the ascending series formula given, particularly for values of |z| near 10.

Running time:
The test run output reproduced at the end of the Long Write Up took 0.207 sec.