Computing zeros and orders of Bessel functions

Yasuhiko Ikebe, Yasushi Kikuchi, Issei Fujishiro

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We consider computing a prescribed number of smallest positive zeros of Bessel functions and of their derivatives of a prescribed order within a prescribed relative error. We also consider an inverse problem of computing the order of the Bessel function that has a zero of a prescribed order at a prescribed positive value. The case of Bessel functions of real noninteger order less than -1 is also discussed. Our emphasis in this paper is on algorithm construction and convergence analysis that will be needed for the construction of software for solving the stated problems.

Original languageEnglish
Pages (from-to)169-184
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume38
Issue number1-3
DOIs
Publication statusPublished - 23 Dec 1991

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Keywords

  • Bessel function
  • Newton's method
  • compact matrix operator
  • eigenvalue problem
  • zeros

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