Evaluation of Abramowitz functions in the right half of the complex plane

Zydrunas Gimbutas, Shidong Jiang, Li Shi Luo

Research output: Contribution to journalArticlepeer-review

Abstract

A numerical scheme is developed for the evaluation of Abramowitz functions Jn in the right half of the complex plane. For n=−1,…,2, the scheme utilizes series expansions for |z|<1, asymptotic expansions for |z|>R with R determined by the required precision, and least squares Laurent polynomial approximations on each sub-region in the intermediate region 1≤|z|≤R. For n>2, Jn is evaluated via a forward recurrence relation. The scheme achieves nearly machine precision for n=−1,…,2 at a cost that is competitive as compared with software packages for the evaluation of other special functions in the complex domain.

Original languageEnglish (US)
Article number109169
JournalJournal of Computational Physics
Volume405
DOIs
StatePublished - Mar 15 2020

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Abramowitz functions
  • Laurent series
  • Least squares method

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