and 
and define the cubic AGM by
which converge cubically to a common limit
where the hypergeometric function 
. In
particular, the hypergeometric function possesses the simple cubic
functional equation 
This can be validated
symbolically once known! As an example 
and 4 iterations of 
will compute the hypergeometric function at
to 25 significant digits. Any direct computation so near the
radius of convergence is doomed.
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