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Calculating Hypergeometric Function 2F1 for z>1 
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#1
May2611, 09:30 AM

P: 21

1. The problem statement, all variables and given/known data
I'm need to integrate the function [tex]\frac{A}{(1+B^2x^2)^{\frac{C+1}{2}}}[/tex] which using wolfram alpha gives a function of the 'hypergeometric function' [tex]_2F_1(a,b;c;z)[/tex] [tex]Ax_2F_1(\frac{1}{2},\frac{C+1}{2};\frac{3}{2};B^2x^2)[/tex] 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 [tex]\leftB^2x^2\right> 1[/tex] 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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