Numerische Mathematik

, Volume 59, Issue 1, pp 647–657

An approximation for the zeros of Bessel functions

  • Á. Elbert
Article

DOI: 10.1007/BF01385801

Cite this article as:
Elbert, Á. Numer. Math. (1991) 59: 647. doi:10.1007/BF01385801

Summary

LetCvk be thekth positive zero of the cylinder functionCv(x)=cosαJv(x)−sinαYv(x), whereJv(x),Yv(x) are the Bessel functions of first kind and second kind, resp., andv>0, 0≦α<π. Definejvk byjvk=Cvk with\(\kappa = k - \frac{\alpha }{\pi }\). Using the notation 1/K=ε, we derive the first two terms of the asymptotic expansion ofjvk in terms of the powers of ε at the expense of solving a transcendental equation. Numerical examples are given to show the accuracy of this approximation.

Mathematics Subject Classification (1991)

65H05

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Á. Elbert
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary