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Re: Beta function, Integral

  • To: mathgroup at
  • Subject: [mg79891] Re: Beta function, Integral
  • From: "David W.Cantrell" <DWCantrell at>
  • Date: Wed, 8 Aug 2007 04:49:00 -0400 (EDT)
  • References: <f990ds$btq$>

Asim <maa48 at> wrote:
> 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])}

What version are you using?

First, note that the reason you're getting your answer in braces, rather
than just the answer --  i.e. {antiderivative}, rather than just the
antiderivative -- is that you put your first exponent in braces, rather
than parentheses.

With that problem fixed, then in version 5.2, the result is

Gamma[p] Gamma[q]/Gamma[p + q].

The antiderivative you got is equivalent to that and also to Beta[p,q].
Thus, there is no bug.


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