ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 08 Jul 2014 11:02:16 -0500integration ends up with hypergeometric function can not be done by sagehttp://ask.sagemath.org/question/10617/integration-ends-up-with-hypergeometric-function-can-not-be-done-by-sage/we know the integration of
1/(a^b+1)
with respect to a is going to get
2F1(1,1/a,1+1/a,-a^x)
where 2f1 is hypogeometric function. However, once we to that in sage, it is not possible to get results
sage: integrate(1/(x^b+1),x)
integrate(1/(x^b + 1), x)
hope this can be fixed up latter or have some alternative way to work around.
Wed, 16 Oct 2013 13:57:57 -0500http://ask.sagemath.org/question/10617/integration-ends-up-with-hypergeometric-function-can-not-be-done-by-sage/Answer by Shashank for <p>we know the integration of </p>
<pre><code>1/(a^b+1)
</code></pre>
<p>with respect to a is going to get</p>
<p>2F1(1,1/a,1+1/a,-a^x)</p>
<p>where 2f1 is hypogeometric function. However, once we to that in sage, it is not possible to get results</p>
<pre><code>sage: integrate(1/(x^b+1),x)
integrate(1/(x^b + 1), x)
</code></pre>
<p>hope this can be fixed up latter or have some alternative way to work around. </p>
http://ask.sagemath.org/question/10617/integration-ends-up-with-hypergeometric-function-can-not-be-done-by-sage/?answer=15549#post-id-15549It seems sage's default algorithm can't do it. You can use mathematica's algorithm to do it in sage. You don't need mathematica installed on you computer. Just type the following command.
b=var('b')
integral(1/(x^b+1),x,algorithm='mathematica_free')Wed, 16 Oct 2013 14:54:34 -0500http://ask.sagemath.org/question/10617/integration-ends-up-with-hypergeometric-function-can-not-be-done-by-sage/?answer=15549#post-id-15549Answer by kcrisman for <p>we know the integration of </p>
<pre><code>1/(a^b+1)
</code></pre>
<p>with respect to a is going to get</p>
<p>2F1(1,1/a,1+1/a,-a^x)</p>
<p>where 2f1 is hypogeometric function. However, once we to that in sage, it is not possible to get results</p>
<pre><code>sage: integrate(1/(x^b+1),x)
integrate(1/(x^b + 1), x)
</code></pre>
<p>hope this can be fixed up latter or have some alternative way to work around. </p>
http://ask.sagemath.org/question/10617/integration-ends-up-with-hypergeometric-function-can-not-be-done-by-sage/?answer=15550#post-id-15550Correct - see [Trac 2516](http://trac.sagemath.org/ticket/2516) for the current status.
See [this Bessel function doc](http://sagemath.org/doc/reference/functions/sage/functions/bessel.html?highlight=bessel#sage.functions.bessel.Function_Bessel_J) for an example that might help you by using Maxima more directly in your own context.
sage: m = maxima(bessel_J(2, x))
sage: m.integrate(x)
hypergeometric([3/2],[5/2,3],-x^2/4)*x^3/24
Also related - [Trac 9908](http://trac.sagemath.org/ticket/9908).Wed, 16 Oct 2013 14:59:49 -0500http://ask.sagemath.org/question/10617/integration-ends-up-with-hypergeometric-function-can-not-be-done-by-sage/?answer=15550#post-id-15550Comment by kcrisman for <p>Correct - see <a href="http://trac.sagemath.org/ticket/2516">Trac 2516</a> for the current status.</p>
<p>See <a href="http://sagemath.org/doc/reference/functions/sage/functions/bessel.html?highlight=bessel#sage.functions.bessel.Function_Bessel_J">this Bessel function doc</a> for an example that might help you by using Maxima more directly in your own context.</p>
<pre><code>sage: m = maxima(bessel_J(2, x))
sage: m.integrate(x)
hypergeometric([3/2],[5/2,3],-x^2/4)*x^3/24
</code></pre>
<p>Also related - <a href="http://trac.sagemath.org/ticket/9908">Trac 9908</a>.</p>
http://ask.sagemath.org/question/10617/integration-ends-up-with-hypergeometric-function-can-not-be-done-by-sage/?comment=23267#post-id-23267Though apparently Maxima can't do this particular integral either.Tue, 08 Jul 2014 11:02:16 -0500http://ask.sagemath.org/question/10617/integration-ends-up-with-hypergeometric-function-can-not-be-done-by-sage/?comment=23267#post-id-23267