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abelian function (Definition)

An abelian or hyperelliptic function is a generalisation of an elliptic function. It is a function of two variables with four periods. In a similar way to an elliptic function it can also be regarded as the inverse function to certain integrals (called abelian or hyperelliptic integrals) of the form $$\int\frac{dz}{R(z)} $$ where $R$ is a polynomial of degree greater than 4.




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Other names:  hyperelliptic function
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Cross-references: degree, polynomial, integrals, inverse function, similar, periods, variables, function, elliptic function, abelian

This is version 2 of abelian function, born on 2004-10-10, modified 2005-03-04.
Object id is 6354, canonical name is AbelianFunction2.
Accessed 3577 times total.

Classification:
AMS MSC26-00 (Real functions :: General reference works )

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