BIT Numerical Mathematics

, Volume 2, Issue 4, pp 232–255

An arsenal of ALGOL procedures for complex arithmetic

Article

DOI: 10.1007/BF01940171

Cite this article as:
Wynn, P. BIT (1962) 2: 232. doi:10.1007/BF01940171

Abstract

This paper contains a complete system of ALGOL procedures which enable arithmetic operations to be carried out upon complex numbers. Further procedures for carrying out the evaluation of certain elementary functions (e.g. ln, exp, sin, ...) of a complex variable are given. Application of these procedures is then illustrated by their use in the computation of the confluent hypergeometric function and the Weber parabolic cylinder function. Procedures relating to the application of the ε-algorithm to series of complex terms are described. Two integrated series of procedures, relating to Stieltjes typeS-fractions and to corresponding continued fractions respectively, are given. Complete programmes, which illustrate the use of these procedures, may be used for the computation of the incompleteβ-function, the incompleteΓ-function (of arguments of large and small modulus) and the Weber function.

Copyright information

© BIT Foundations 1962

Authors and Affiliations

  • P. Wynn
    • 1
  1. 1.Mathematisch CentrumAmsterdam