Zeros of the Macdonald function of complex order

Authors:
Erasmo M. Ferreira;Javier Sesma
Affiliations:
Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, RJ, Brazil;Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

The z-zeros of the modified Bessel function of the third kind K"@n(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order @n. Approximate expressions for the zeros, applicable in the cases of very small or very large |@n|, are given. The behaviour of the zeros for varying |@n| or arg@n, obtained numerically, is illustrated by means of some graphics.