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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 \(\left\{ {{a_n}} \right\}_{n = 0}^\infty \) and \(\left\{ {{b_n}} \right\}_{n = 0}^\infty \) determined by the algorithm
$${a_0} = a,\,{b_0} = b, $$
$${a_{n + 1}} = \left( {{a_n} + {b_n}} \right)/2,\,{b_{n + 1}} = {\left( {{a_n}{b_n}} \right)^{1/2}},\,n = 0,1,2, \ldots \,.$$
(0.1)

Keywords

Modular Form Theta Function Fundamental Domain Modular Function Elliptic Integral 
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 2000

Authors and Affiliations

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

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