skip to main content
article
Free Access

Symbolic computation of residues at poles and essential singularities

Published:01 February 1982Publication History
Skip Abstract Section

Abstract

Although most books on the theory of complex variables include a classification of the types of isolated singularities, and the applications of residue theory, very few concern themselves with methods of computing residues. In this paper we derive some results on the calculation of residues at poles, and some special classes of essential singularities, with a view to implementing an algorithm in the VAXIMA computer algebra system.

References

  1. John K. Foderaro, The FRANZ LISP manual, the University of California, 1980.Google ScholarGoogle Scholar
  2. J. K. Foderaro and R. J. Fateman, Characterisation of VAX Macsyma, Proceedings, ACM SYMSAC '81 Conference, Snowbird, Utah, August 5-7, 1981, pp. 14--19. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. A. R. Forsyth, Theory of Functions of a Complex Variable, Vol. I, Dover publications, 1965.Google ScholarGoogle Scholar
  4. P. Henrici, Applied and Computational Complex Analysis, Vol. I, Wiley-Interscience, 1974.Google ScholarGoogle Scholar
  5. The Mathlab Group Laboratory for Computer Science, MACSYMA Reference Manual, VERSION NINE, Second Printing, December 1977.Google ScholarGoogle Scholar
  6. M. R. Spiegel, Advanced Calculus (Schaum's Outline series), Mcgraw-Hill, 1974.Google ScholarGoogle Scholar
  7. M. R. Spiegel, Complex Analysis (Schaum's Outline series), Mcgraw-Hill, 1964Google ScholarGoogle Scholar
  8. Paul S. Wang, Symbolic Evaluation of Definite Integrals by Residue Theory in MACSYMA, Proceedings, IFIP Congess 74, Stockholm, Sweden, August 5-10, pp. 823--827.Google ScholarGoogle Scholar
  9. Richard E. Zipple, Univarite Power Series Expansions in Algebraic Manipulation, Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation, Yorktown Heights, N.Y., August 10-12, 1976, pp. 198--208. Google ScholarGoogle ScholarDigital LibraryDigital Library

Recommendations

Comments

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Sign in

Full Access

  • Published in

    cover image ACM SIGSAM Bulletin
    ACM SIGSAM Bulletin  Volume 16, Issue 1
    February 1982
    16 pages
    ISSN:0163-5824
    DOI:10.1145/1089297
    Issue’s Table of Contents

    Copyright © 1982 Author

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    • Published: 1 February 1982

    Check for updates

    Qualifiers

    • article

PDF Format

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader