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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