Journal of Applied Mathematics and Computing

, Volume 43, Issue 1–2, pp 151–173 | Cite as

On the calculation of the finite Hankel transform eigenfunctions

  • P. Amodio
  • T. Levitina
  • G. Settanni
  • E. B. Weinmüller
Original Research


In this work, we discuss the numerical computation of the eigenvalues and eigenfunctions of the finite (truncated) Hankel transform, important for numerous applications. Due to the very special behavior of the Hankel transform eigenfunctions, their direct numerical calculation often causes an essential loss of accuracy.

Here, we present several simple, efficient and robust numerical techniques to compute Hankel transform eigenfunctions via the associated singular self-adjoint Sturm-Liouville operator. The properties of the proposed approaches are compared and illustrated by means of numerical experiments.


Finite Hankel transform Generalized spheroidal wave functions Singular Sturm-Liouville problem Finite difference schemes Prüfer angle 

Mathematics Subject Classification (2000)

34B16 34B24 34L16 65F15 65L10 65L15 65R10 65R20 



The authors are very grateful for the warm hospitality of Vienna University of Technology while working on this paper.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2013

Authors and Affiliations

  • P. Amodio
    • 1
  • T. Levitina
    • 2
  • G. Settanni
    • 1
  • E. B. Weinmüller
    • 3
  1. 1.Dipartimento di MatematicaUniversità di BariBariItaly
  2. 2.Institute for Computational MathematicsTU BraunschweigBrunswickGermany
  3. 3.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria

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