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

asked 2013-10-16 20:57:57 +0100

chenming
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updated 2013-10-16 22:00:47 +0100

kcrisman
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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 21:54:34 +0100

Shashank

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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 21:59:49 +0100

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

kcrisman ( 2014-07-08 18:02:16 +0100 )edit

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