# Integration with hypergeometric function

1. Jun 29, 2014

### 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.

2. Jun 29, 2014

### micromass

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

3. Jun 29, 2014

### JulieK

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

4. Jun 29, 2014

### micromass

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

5. Jun 29, 2014

### JulieK

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

6. Jun 29, 2014