# Thread: Free computer algebra system

1. ## Free computer algebra system

I am trying to integrate a very messy expression using Wolfram online integrator but I get the message:
"You need to use Mathematica to evaluate this expression".
The online integrator works only for relatively simple expressions.
Unfortunately I do not have a license for Mathematica.
Any proposal to overcome this?
Is there a free computer algebra software that can be used as a replacement to Mathematica.

2. ## Re: Free computer algebra system

Originally Posted by JulieK
I am trying to integrate a very messy expression using Wolfram online integrator but I get the message:
"You need to use Mathematica to evaluate this expression".
The online integrator works only for relatively simple expressions.
Unfortunately I do not have a license for Mathematica.
Any proposal to overcome this?
Is there a free computer algebra software that can be used as a replacement to Mathematica.
What is the expression you are trying to work out?

-Dan

3. ## Re: Free computer algebra system

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

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

4. ## Re: Free computer algebra system

Try the following input on Wolfram|Alpha: Hypergeometric2F1[1, 2, 1, x^2],for example.

-Dan

5. ## Re: Free computer algebra system

This is not my expression.
When I type an expression similar to my expression (A*x*Hypergeometric2F1[1,2,1,x^2]) in Wolfram Alpha I get a very simple answer which cannot be correct.
I checked this by differentiating the answer.

6. ## Re: Free computer algebra system

Okay, first of all see here for the definition of the hypergeometric function as a series representation.

Your answer is simple because the case I picked is simple. Here's the derivation:
$\displaystyle _2 F _1(1, 2, 1; x^2) = 1 + \sum _{n = 1}^{\infty} \frac{(1)_n \cdot (2)_n}{(1)_n} \frac{\left ( x^2 \right ) ^n}{n!}$

where $\displaystyle (a)_n$ is the "Pochhammer symbol."

$\displaystyle = 1 + \sum_{n = 1}^{\infty} (2)_n \frac{x^{2n}}{n!}$

$\displaystyle = 1 + \sum_{n = 1}^{\infty} \Gamma(2 + n)/ \Gamma(2) \frac{x^{2n}}{n!}$

$\displaystyle = 1 + \sum_{n = 1}^{\infty} (n + 1) x^{2n}$

The summations are simple (I'll show those if you want) giving:

$\displaystyle = 1 + \frac{2x^2 - x^4}{(x^2 - 1)^2}$

$\displaystyle _2 F _1(1, 2, 1; x^2) = \frac{1}{(x^2 - 1)^2}$

-Dan

7. ## Re: Free computer algebra system

1. Many thanks!

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

3. What about my expression, i.e
$\displaystyle _{2}F_{1}(B;C;D;Ex^{2})\,Ax$
Can you do the same for this?

8. ## Re: Free computer algebra system

Originally Posted by JulieK
1. Many thanks!

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

3. What about my expression, i.e
$\displaystyle _{2}F_{1}(B;C;D;Ex^{2})\,Ax$
Can you do the same for this?
I can't help you with the |x| < 1. You might be able to analytically continue it into regions where x is larger, but that is out of my league. As to $\displaystyle Ax \times _2 F _1(B, C, D, Ex^2)$, that's just going to be
$\displaystyle \frac {Ax}{(x^2 - 1)^2}$

I'm not sure what you are trying to do here.

-Dan