# Calculating Hypergeometric Function 2F1 for |z|>1

by mudkip9001
Tags: function, hypergeometric, |z|>1
 P: 21 1. The problem statement, all variables and given/known data I'm need to integrate the function $$\frac{A}{(1+B^2x^2)^{\frac{C+1}{2}}}$$ which using wolfram alpha gives a function of the 'hypergeometric function' $$_2F_1(a,b;c;z)$$ $$Ax_2F_1(\frac{1}{2},\frac{C+1}{2};\frac{3}{2};-B^2x^2)$$ I'm writing a program to calculate the integral at diffent values of x. The problem is that for most of my data, x gives values of $$\left|B^2x^2\right|> 1$$ and it seems that calculating it at those points becomes much more complicated, beyond my mathematical capabilities. 3. The attempt at a solution messing about with wolfram it seems that as long as z<0 the solution is a real number, so it should be possible to calculate it in my program. However the GNU scientific library is only capable of calculating it for |z|<1.

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