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Number Theory pp 493-540 | Cite as

Elliptic Functions

  • W. A. Coppel
Chapter
Part of the Universitext book series (UTX)

Abstract

Our discussion of elliptic functions may be regarded as an essay in revisionism, since we do not use Liouville’s theorem, Riemann surfaces or the Weierstrassian functions. We wish to show that the methods used by the founding fathers of the subject provide a natural and rigorous approach, which is very well suited for applications.

The work is arranged so that the initial sections aremutually independent, although motivation for each section is provided by those which precede it. To some extent we have also separated the discussion for real and for complex parameters, so that those interested only in the real case may skip the complex one.

Keywords

Elliptic Function Theta Function Modular Function Elliptic Integral Positive Real Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • W. A. Coppel
    • 1
  1. 1.GriffithAustralia

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