"It is very tempting to write your own code for Gauss's hypergeometric
function 2F1(a;b;c;z). The definition is just a power series. But
any code that implements the definition using floating point arithmetic
is bound to have terrible numeric properties for large argument.
For example, hypergeom([],[],z) is equal to exp(z) and using the
power series alone to compute exp(z) is well known to be a bad idea.
MATLAB can't do a general hypergeom reliably using only floating
point so we have Maple do it for us, using arithmetic with as many
digits as necessary to get accurate answers.
I would be very suspicious of anybody who claims to have fast code
for hypergeometric series.
-- Cleve
moler@mathworks.com "
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