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# Functions, Abelian

• ### Variants

• Abelian functions
• Abelian integrals
• Hyper-elliptic integrals
• Hyperelliptic functions
• Hyperelliptic integrals
• Integrals, Abelian

• ### Sources

• found: Encyc. math.(a generalization of the concept of an elliptic function of one complex variable to the case of several complex variables)
• found: Eric Weisstein's world of mathematics, via WWW, Jan. 27, 2003:Abelian function (an inverse function of an Abelian integral; Abelian functions are a generalization of elliptic functions, and are also called hyperelliptic functions) Abelian integral (also called hyperelliptic integrals)
• found: Encyc. of mathematics on CD-ROM, 1997:hyper-elliptic integral (the special case of an Abelian integral)
• found: The MacTutor history of mathematics archive, via WWW, Jan. 30, 2003:index of glossary terms (Abelian or hyperelliptic function. 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 [integral of] dz/[square root of] R(z) where R is a polynomial of degree greater than 4)

• QA345
• ### Change Notes

• 2003-01-31: new
• 2003-03-17: revised

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