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