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The Arithmetic-Geometric Mean of Gauss

  • David A. Cox
Chapter

Abstract

The arithmetic-geometric mean of two numbers a and b is defined to be the common limit of the two sequences {a n } n = 0 and {b n } n = 0 determinec by the algorithm
$$\begin{array}{l} {a_0} = a,\quad \quad \quad \quad \quad \quad {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {b_0} = b, \\ {a_{n + 1}} = \left( {{a_n} + {b_n}} \right)/2,\;\quad \quad {b_{n + 1}} = {\left( {{a_n}{b_n}} \right)^{1/2}},\quad n = 0,1,2, \ldots \\ \end{array}$$
(0.1)

Keywords

Modular Form Elliptic Function Theta Function Fundamental Domain Modular Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • David A. Cox
    • 1
  1. 1.Department of MathematicsAmherst CollegeAmherstUSA

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