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Re: Odd results in integration

• To: mathgroup at smc.vnet.net
• Subject: [mg32897] Re: Odd results in integration
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Mon, 18 Feb 2002 05:22:28 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <a4la4q$e1h$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

Integrate[(a - y)^(2*n - 1)/(b - y)^n, y] // FullSimplify

and

Integrate[(\[Alpha] - y)^(2*n - 1)/(\[Beta] - y)^n, y] // FullSimplify

generate the same output. On the first look, the results without
the FullSimplify[] seems to be different because Mathematica use
a different symbol ordering for a,b,y and \[Alpha],\[Beta], y

Regards
  Jens

Tomas Garza wrote:
> 
> 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.
> 
> Tomas Garza
> Mexico City