I want to calculate the function
gg[m, x] given by
gg[m_, x_] := Hypergeometric2F1[2 + m, 5/2 + m, 2 + 2 m, x^2]
x is between 1 and 0. I need to calculate this function with high values of
1000 <= m <= 2000).
In some regions the calculation gives the result quickly. For example, when
x is between 0, and .66, the speed of calculation is fast. Further, by using
$MaxExtraPrecision = Infinity, I can calculate
gg in the region
.8 < x <. 999 quickly, However, in the region
.72 < x < .80, it gets very slow. At
x = .77 the calculation takes nearly a day to finish.
I want to know how can I eliminate this hindrance to my calculations. I must mention that I give x as a rational number, say, 66/100 or 77/100, because I want to avoid machine arithmetic.