Symbolic and numerical computation on Bessel functions of complex argument and large magnitude

Jun Zhang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The Lanczos τ-method, with perturbations proportional to Faber polynomials, is employed to approximate the Bessel functions of the first kind Jv(z) and the second kind Fv(z), the Hankel functions of the first kind H(1)v(z) and the second kind H(2)v(z) of integer order v for specific outer regions of the complex plane, i.e. |z| ≥ R for some R. The scaled symbolic representation of the Faber polynomials and the appropriate automated τ-method approximation are introduced. Both symbolic and numerical computation are discussed. In addition, numerical experiments are employed to test the proposed τ-method. Computed accuracy for J0(z) and for |Z| ≥ 8 are presented. The results are compared with those obtained from the truncated Chebyshev series approximations and with those of the τ-method approximations on the inner disk |z| ≤ 8. Some concluding remarks and suggestions on future research are given.

Original languageEnglish
Pages (from-to)99-118
Number of pages20
JournalJournal of Computational and Applied Mathematics
Issue number1
StatePublished - Nov 12 1996


  • Automated τ-method
  • Bessel functions
  • Chebyshev series
  • Symbolic Faber polynomials

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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