Zeros of the Macdonald function of complex order

2006/07/31 by Erasmo M. Ferreira, Javier Sesma, J. Sesma · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Mathematical functions and polynomials #Matrix Theory and Algorithms #math.CA #msc:33C10

paper · pdf · doi:10.1016/j.cam.2006.11.014

published as J. Comput. Appl. Math. 211 (2008) 223-231 · 14 pages, 3 figures, 1 table. Added a table illustrating the numerical procedure

arxiv created 2006/11/14 · openalex publication_date 2006/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

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

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• Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of K iν (z) with Respect to Order
• On an identity for zeros of Bessel functions