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

1 Scopus citations


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
StatePublished - Mar 15 2020

All Science Journal Classification (ASJC) codes

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


  • Abramowitz functions
  • Laurent series
  • Least squares method


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