Zeros of the Macdonald function of complex order

The z-zeros of the modified Bessel function of the third kind K ν ( z ) , also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order ν . Approximate expressions for the zeros, applicable in the cases of very small or very large | ν | , are...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2008-02, Vol.211 (2), p.223-231
Main Authors: Ferreira, Erasmo M., Sesma, Javier
Format: Article
Language:English
Subjects:
Exact sciences and technology
Hankel function
Macdonald function
Mathematical analysis
Mathematics
Modified Bessel function of the third kind
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Special functions
Zeros
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Summary:The z-zeros of the modified Bessel function of the third kind K ν ( z ) , also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order ν . Approximate expressions for the zeros, applicable in the cases of very small or very large | ν | , are given. The behaviour of the zeros for varying | ν | or arg ν , obtained numerically, is illustrated by means of some graphics.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2006.11.014