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integration ends up with hypergeometric function can not be done by sage

asked 2013-10-16 13:57:57 -0500

chenming gravatar image

updated 2013-10-16 15:00:47 -0500

kcrisman gravatar image

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.

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answered 2013-10-16 14:54:34 -0500

Shashank gravatar image

It 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')
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answered 2013-10-16 14:59:49 -0500

kcrisman gravatar image

Correct - see Trac 2516 for the current status.

See this Bessel function doc 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.

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Comments

Though apparently Maxima can't do this particular integral either.

kcrisman gravatar imagekcrisman ( 2014-07-08 11:02:16 -0500 )edit

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Asked: 2013-10-16 13:57:57 -0500

Seen: 395 times

Last updated: Oct 16 '13