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Manuscript Title: Accurate Bessel functions Jn(z), Yn(z), H(1)n(z) and H(2)n(z) of integer order and complex argument.
Authors: R.W.B. Ardill, K.J.M. Moriarty
Program title: BESJYH
Catalogue identifier: ACYQ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 17(1979)321
Programming language: Fortran.
Computer: CDC 6600, CDC 7600.
Operating system: CDC NOS/BE, SCOPE.
RAM: 6K words
Word size: 60
Keywords: General purpose, Expansion, Representation, Eikonal, Impact parameter, Helicity, Partial wave, Bessel function, Kelvin function, Neumann function, Weber's function, Hankel function, Complex function.
Classification: 4.7.

Revision history:
Type Tit le Reference
correction 000A CORRECTION 30/09/85 See below

Nature of problem:
The Bessel function appears in a wide range of physical applications, and in particular where there is axial symmetry. The package contains complex function routines to calculate Jn(z), Yn(z), Hn**(1)(z) and Hn**(2)(z) for integer n and complex z.

Solution method:
The method of solution is based on the ascending series representations and asymptotic forms of the Bessel functions Jn(z) and Yn(z) and asymptotic forms of the modified Bessel functions In(z) and Kn(z).

Restrictions:
The program will return results for all values of |z| up to machine overflows in the Bessel functions. The size of the order should not be too large (say,|n|<=15) or accuracy will be lost. For large |n|, the user should incorporate into the program the formulae given for Debye's asymptotic expansions or better, the uniform asymptotic expansions. The value of the relative accuracy parameter, EPS, should not be set below about 10**-11. For the asymptotic region, the accuracy EPS may not always be achieved (since the asymptotic series may have to be truncated at their lower terms), in which case the output parameter ISET will indicate this and an estimation of the relative error is also produced. The functions Yn(z), H(1)n(z) and H(2)n(z) have a branch point at the origin, together with a cut along the negative real axis.

Running time:
The test run output at the end of the Long Write Up took about 4.2 s.

CORRECTION SUMMARY
Manuscript Title: Accurate Bessel functions Jn(z), Yn(z), H(1)n(z) and H(2)n(z) of integer order and complex argument. (C.P.C. 17(1979)321).
Authors: R.W.B. Ardill, K.J.M. Moriarty
Program title: 000A CORRECTION 30/09/85
Catalogue identifier: ACYQ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 39(1986)303
Classification: 4.7.