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Manuscript Title: Determination of nu-zeros of Hankel functions.
Authors: J.B. Campbell
Program title: NUZERO
Catalogue identifier: ACCH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 32(1984)333
Programming language: Fortran.
Computer: IBM 3081.
Operating system: TSS/370.
RAM: 7K words
Word size: 32
Keywords: General purpose, Scattering, Diffraction, Bessel, Hankel, Zeros.
Classification: 4.7.

Nature of problem:
The nu-zeros of the equations: Hnu(1)(z) = 0, (d/dz)Hnu(1)(z) = 0, (d/dz)Hnu(1)(z) + iWHnu(1)(z) = 0, where Hnu(1)(z) is a Hankel function, are of interest in electromagnetic theory in numerous scattering and diffraction problems with circular or spherical boundaries.

Solution method:
Muller's iteration method for algebraic equations is used to determine the zeros. An approximation to the first two zeros is obtained from an appropriate asymptotic expression. Approximations to the remaining zeros are obtained either by extrapolation or from an asymptotic expression. The Hankel functions are calculated either from Neumann series or from a continued fraction representation.

The real and imaginary parts of z and W are assumed to be non-negative. The program determines zeros accurately only for |z|<=15. For |z|>15, the program produces zeros from their asymptotic expression for large |z|. A zero is not determined unless its first approximation Nuo has Re(Nuo)<=27 and Im(Nuo)<=27.

Running time:
The determination of a sequence of 10 zeros requires approximately 200 ms. for typical values of the arguments. (Accuracy, approximately 10 digits).