Integration with hypergeometric function

[JulieK]

How to integrate:

$_{2}F_{1}(B;C;D;Ex^{2})\,Ax$

where $_{2}F_{1}(...)$ is the hypergeometric function, x is the independent variable and A, B, C, D, and E are constants.

 

[micromass]

Can you write $${}_2F_1(B,C;D;Ex^2)Ax$$ as a (power) series? Do you know how to integrate a power series?

 

[JulieK]

I am familiar with the power series method but I am trying first to find a simpler and more compact method.

 

[micromass]

I am familiar with the power series method but I am trying first to find a simpler and more compact method.

Since the hypergeometric function ${}_2F_1$ is defined as a power series, it is hard to imagine a solution that avoids it.

 

[JulieK]

One problem with the power series is that it is defined only for |x|<1.

 

[JJacquelin]

See : http://www.wolframalpha.com/input/?i=Integrate+hypergeometric2F1(B,C,D,E*x^2)*A*x*dx
A first step : change of variable X=x²