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2 results

  • Cubic and Higher Order Algorithms for π

  • J. M. Borwein, P. B. Borwein
  • Journal:
    Canadian Mathematical Bulletin / Volume 27 / Issue 4 / 01 December 1984
    Published online by Cambridge University Press:
    20 November 2018, pp. 436-443
    Print publication:
    01 December 1984
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  • We show that the theory of elliptic integral transformations may be employed to construct iterative approximations for π of order p (p any prime). Details are provided for two, three and seven. The cubic case proves amenable to surprisingly complete analysis.

  • The group of automorphisms of a differential algebraic function field

  • Michihiko Matsuda
  • Journal:
    Nagoya Mathematical Journal / Volume 74 / July 1979
    Published online by Cambridge University Press:
    22 January 2016, pp. 87-94
    Print publication:
    July 1979
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  • Consider a one-dimensional differential algebraic function field K over an algebraically closed ordinary differential field k of characteristic 0. We shall prove the following theorem:

    Suppose that the group of all automorphisms of K over k is infinite. Then, K is either a differential elliptic function field over k or K = k(ν) with ν′ = ξ or ν′ = ην, where ξ, η ϵ k.