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MathGroup Archive 2007

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Re: Beta function, Integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79886] Re: Beta function, Integral
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Wed, 8 Aug 2007 04:46:22 -0400 (EDT)
  • References: <f990ds$btq$1@smc.vnet.net>
  • Reply-to: "Dr. Wolfgang Hintze" <weh at snafu.de>

I'm getting
In[12]:=
$Version
Out[12]=
"5.2 for Microsoft Windows (June 20, 2005)"

In[1]:=
Integrate[t^{p - 1}*(1 - t)^(q - 1), {t, 0, 1},
Assumptions -> {p > 0, q > 0}]
Out[1]=
{(Gamma[p]*Gamma[q])/Gamma[p + q]}

which is what we would expect (Euler's Beta function written in terms 
of Gamma functions)
but which is also equivalent to your result because of

In[11]:=
eq = FullSimplify[Gamma[q] ==
Pi*(Csc[Pi*q]/Gamma[1 - q])]
Out[11]=
True

Hence no wrongdoing, no bug - simply inconvenience!

Regards,
Wolfgang


"Asim" <maa48 at columbia.edu> schrieb im Newsbeitrag 
news:f990ds$btq$1 at smc.vnet.net...
>
> Hi
>
> The following integral does not seem to give the correct answer. The
> answer should be the Euler Beta function,  Beta[p,q]. Can anybody let
> me know what I am doing wrong? Or is this a bug?
>
>
> In[12]:= Integrate[t^{p - 1}*(1 - t)^(q - 1), {t, 0, 1}, 
>  Assumptions -
>> {p > 0, q > 0}]
>
> Out[12]= {(\[Pi] Csc[\[Pi] q] Gamma[p])/(Gamma[1 - q] Gamma[p + q])}
>
>
> Thanks
>
> Asim Ansari
>
> 



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