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us: Functions, Abelian


  • URI(s)

  • Instance Of

  • Scheme Membership(s)

  • Collection Membership(s)

  • Variants

    • us: Abelian functions
    • us: Abelian integrals
    • us: Hyper-elliptic integrals
    • us: Hyperelliptic functions
    • us: Hyperelliptic integrals
    • us: Integrals, Abelian
  • Broader Terms

    • us: Elliptic functions
    • us: Functions of complex variables
  • 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)
  • LC Classification

    • QA345
  • Change Notes

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

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