The Arithmetic-Geometric Mean of Gauss

  • David A. Cox


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
$${a_0} = a,\,{b_0} = b, $$
$${a_{n + 1}} = \left( {{a_n} + {b_n}} \right)/2,\,{b_{n + 1}} = {\left( {{a_n}{b_n}} \right)^{1/2}},\,n = 0,1,2, \ldots \,.$$


Modular Form Theta Function Fundamental Domain Modular Function Elliptic Integral 
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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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