Numerical techniques for finding -zeros of Hankel functions

Authors:
James Alan Cochran and Judith N. Hoffspiegel

Journal:
Math. Comp. **24** (1970), 413-422

MSC:
Primary 65.25

DOI:
https://doi.org/10.1090/S0025-5718-1970-0272157-6

MathSciNet review:
0272157

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Abstract: This paper is concerned with numerical procedures for the evaluation of the zeros, with respect to order, of Hankel functions and their derivatives in cases when the arguments of these functions are held fixed. Using Olver's asymptotic expansions, two auxiliary tables have been computed, one appropriate for real and the other for purely imaginary argument. These tables, included herein, permit the calculation of rather accurate approximations to the desired -zeros for wide ranges of argument and index. Moreover, from the given tabular entries, the errors attendant with any approximate -zero so determined can be easily estimated.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0272157-6

Keywords:
Special functions,
cylindrical functions,
Bessel functions,
Hankel functions,
rootfinding,
numerical approximation,
function evaluation,
asymptotic expansions,
electromagnetic scattering,
creeping-wave propagation

Article copyright:
© Copyright 1970
American Mathematical Society