Calculating Hypergeometric Function 2F1 for |z|>1


by mudkip9001
Tags: function, hypergeometric, |z|>1
mudkip9001
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#1
May26-11, 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]\left|B^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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