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MathGroup Archive 2002

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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


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