Re: Odd results in integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg32880] Re: [mg32871] Odd results in integration*From*: BobHanlon at aol.com*Date*: Mon, 18 Feb 2002 05:21:59 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 2/16/02 5:34:11 AM, tgarza01 at prodigy.net.mx writes: >This problem has been brought to my attention, and I am puzzled as to >what's going on. The following indefinite integral is readily evaluated > >by Mathematica: > >In[1]:= >Integrate[(a - y)^(2*n - 1)/(b - y)^n, y] >Out[1]= >((a - y)^(2*n)*(-b + y)*Hypergeometric2F1[1 - n, 1 - 2*n, > 2 - n, -((b - y)/(a - b))])/(((-a + b)*(-1 + n))* > ((1 + (b - y)/(a - b))^(2*n)*(b - y)^n)) > >where a, b and n are constants. However, if in the above input cell one > >uses the greek letters "alfa" and "beta" (through Esc a Esc and Esc b >Esc) instead of a and b, respectively, the result turns out to be >different. > Other than some cosmetic differences caused by the ordering of the variables, I get the same result for both on my system. $Version 4.1 for Mac OS X (November 5, 2001) soln1 = Integrate[(a - y)^(2*n - 1)/(b - y)^n, y]; soln2 = Integrate[(\[Alpha] - y)^(2*n - 1)/(\[Beta] - y)^n, y]; soln1 == (soln2 /. {\[Alpha]->a, \[Beta]->b}) True You might find it easier to compare the results if you use FullSimplify on each. Bob Hanlon Chantilly, VA USA