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

Zydrunas Gimbutas; Shidong Jiang; Li Shi Luo

doi:10.1016/j.jcp.2019.109169

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

Zydrunas Gimbutas, Shidong Jiang, Li Shi Luo

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A numerical scheme is developed for the evaluation of Abramowitz functions J_n 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, J_n 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 language	English (US)
Article number	109169
Journal	Journal of Computational Physics
Volume	405
DOIs	https://doi.org/10.1016/j.jcp.2019.109169
State	Published - 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

Keywords

Abramowitz functions
Laurent series
Least squares method

Access to Document

10.1016/j.jcp.2019.109169

Cite this

@article{bd8f04bf5e0c45588314bb2b4cc86c3b,

title = "Evaluation of Abramowitz functions in the right half of the complex plane",

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.",

keywords = "Abramowitz functions, Laurent series, Least squares method",

author = "Zydrunas Gimbutas and Shidong Jiang and Luo, {Li Shi}",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

month = mar,

day = "15",

doi = "10.1016/j.jcp.2019.109169",

language = "English (US)",

volume = "405",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Evaluation of Abramowitz functions in the right half of the complex plane

AU - Gimbutas, Zydrunas

AU - Jiang, Shidong

AU - Luo, Li Shi

PY - 2020/3/15

Y1 - 2020/3/15

N2 - 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.

AB - 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.

KW - Abramowitz functions

KW - Laurent series

KW - Least squares method

UR - http://www.scopus.com/inward/record.url?scp=85078010856&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85078010856&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2019.109169

DO - 10.1016/j.jcp.2019.109169

M3 - Article

AN - SCOPUS:85078010856

SN - 0021-9991

VL - 405

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 109169

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this