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[parent] order of an elliptic function (Definition)

The order of an elliptic function is the number of poles of the function contained within a fundamental period parallelogram, counted with multiplicity. Sometimes the term ``degree'' is also used -- this usage agrees with the theory of Riemann surfaces.

This order is always a finite number; this follows from the fact that a meromorphic function can only have a finite number of poles in a compact region (such as the closure of a period parallelogram). As it turns out, the order can be any integer greater than 1.




"order of an elliptic function" is owned by rspuzio.
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possible orders of elliptic functions (Theorem) by rspuzio
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Cross-references: integer, closure, region, compact, meromorphic, finite, Riemann surfaces, theory, term, multiplicity, parallelogram, period, contained, function, poles, number, elliptic function, order
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This is version 5 of order of an elliptic function, born on 2006-03-07, modified 2006-03-25.
Object id is 7694, canonical name is OrderOfAnEllipticFunction.
Accessed 1239 times total.

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AMS MSC33E05 (Special functions :: Other special functions :: Elliptic functions and integrals)

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