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Topic: A bug in Reduce package 'algint'?
Replies: 9   Last Post: Feb 1, 2013 6:02 PM

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 clicliclic@freenet.de Posts: 1,245 Registered: 4/26/08
Re: A bug in Reduce package 'algint'?
Posted: Jan 21, 2013 4:29 PM

Axel Vogt schrieb:
>
> On 21.01.2013 19:55, clicliclic@freenet.de wrote:

> >
> > Wanting to refresh my knowledge of the capabilties of the Reduce algebra
> > system, I have recently browsed the website. The system comes with the
> > 'algint' package by J. Davenport which boosts the integrator
> > capabilities for algebraic functions. The package documentation
> >
> > <http://www.reduce-algebra.com/docs/algint.pdf>
> >
> > introduces the example integrand sqrt(sqrt(a^2 + x^2) + x)/x. A correct
> > antiderivative for this is
> >
> > 2*(sqrt(sqrt(a^2 + x^2) + x)
> > - sqrt(a)*atanh(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a))
> > - sqrt(a)*atan(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a)))
> >
> > The antiderivative printed in the documentation, however, is either very
> > wrong or garbled beyond recognition.
> >

>
> Maple 16 returns 2*sqrt(2*x)*hypergeom([-1/4, -1/4, 1/4],[1/2, 3/4],-a^2/x^2)
> May be right, but not that 'usefull' w.r.t. your result

Oh dear, yes, this is a hypergeometric three-eff-two.

Martin.