Date: Nov 15, 2013 6:11 PM
Author: Albert D. Rich
Subject: Re: The A. F. Timofeev symbolic integration test suite
On Friday, November 15, 2013 3:43:59 AM UTC-10, clicl...@freenet.de wrote:

>> Ok, for integrands of the form (c+d x)^n/(a+b x) when n is symbolic,

>> the next version of Rubi will return

>>

>> (c+d*x)^n/(b*n*(b*(c+d*x)/(d*(a+b*x)))^n)*

>> 2F1(-n,-n,1-n,-(b*c-a*d)/(d*(a+b*x)))

>>

> > The simpler equivalent rule derived using Euler's transformation is

>> not used since it is harder to simplify its derivative back to the

>> original integrand.

> But this is just an arbitrary property of the differentiator, right?

> Another differentiator may give the result you would now obtain by

> applying Euler's transformation first (and undoing it on non-elementary

> hypergeometrics that remain in the derivative).

>

> So your reason is no good reason; you are just bending to the dictate of

> WRI. I suggest that Rubi redefines 2F1 differentiation instead. The

> optimality of Rubi's antiderivatives determines the rules to which WRI

> must bend!

>

> I have spoken.

>

> Martin.

Ok, the Messiah has spoken. I modified the optimal antiderivatives for Timofeev Chapter 8 examples 6a.n, 6b.n and 14 in the test-suite to reflect use of Euler's transformation and posted the revised pdf file at

http://www.apmaths.uwo.ca/~arich/TimofeevChapter8TestResults.pdf

However, full credit is still given to those integrators that return valid, but suboptimal, antiderivatives for these problems.

Note that the revised pdf file also includes Chapter 8 test-suite results for various integrators, including the forthcoming version 4.3 of Rubi...

Albert