ELLIPTICFUNCTION

Elliptic function

In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions. Just as a periodic function of a real variable is defined by its values on an interval, an elliptic function is determined by its values on a fundamental parallelogram, which then repeat in a lattice. Such a doubly periodic function cannot be holomorphic, as it would then be a bounded entire function, and by Liouville's theorem every such function must be constant. In fact, an elliptic function must have at least two poles in a fundamental parallelogram, as it is easy to show using the periodicity that a contour integral around its boundary must vanish, implying ...

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elliptic function

Noun

  1. Any function of a complex variable which is periodic in two directions


The above text is a snippet from Wiktionary: elliptic function
and as such is available under the Creative Commons Attribution/Share-Alike License.

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