Difference between revisions of "Elliptic function"
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Revision as of 21:20, 6 June 2015
A function $f$ is called elliptic if it is a doubly periodic function and it is meromorphic.
Properties
Theorem: All constant functions are elliptic functions.
Proof: █
Theorem: A nonconstant elliptic function has a fundamental pair of periods.
Proof: █
Theorem: If an elliptic function $f$ has no poles in some period parallelogram, then $f$ is a constant function.
Proof: █
Theorem: If an elliptic function $f$ has no zeros in some period parallelogram, then $f$ is a constant function.
Proof: █
Theorem: The contour integral of an elliptic function taken along the boundary of any cell equals zero.
Proof: █
