A method for the computation of the error function of a complex variable-Reference-Cited by-同舟云学术

A method for the computation of the error function of a complex variable

Published:1965 Issue:89 Volume:19 Page:127-129
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Strand Otto Neall

Abstract

This paper presents a method of computing z ≡ ( 2 / π ) ∫ 0 z e − u 2 d u z \equiv \left ( {2/\sqrt \pi } \right )\int _0^z {{e^{ - {u^2}}}du} , where z z is complex. It is shown that z ≡ 1 − erf z z \equiv 1 - {\text {erf }}z has no zeros in the right-hand half plane. An estimate of | erfc z | |{\text {erfc }}z| is derived.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1965-19-089/S0025-5718-1965-0170456-8/S0025-5718-1965-0170456-8.pdf

Reference10 articles.

1. Formulas for calculating the error function of a complex variable;Salzer, H. E.;Math. Tables Aids Comput.,1951

2. On the error function of a complex argument;Kestin, Joseph;Z. Angew. Math. Phys.,1956

3. K. A. Karpov, Tables of the Function 𝑤(𝑧)=𝑒^{-𝑧²}∫₀^{𝑧}𝑒^{𝑥²}𝑑𝑥 in a Complex Region, Izdat. Akad. Nauk SSSR, Moscow, 1954. (Russian) MR 16, 749.

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