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Re: Beta function, Integral
*To*: mathgroup at smc.vnet.net
*Subject*: [mg79891] Re: Beta function, Integral
*From*: "David W.Cantrell" <DWCantrell at sigmaxi.net>
*Date*: Wed, 8 Aug 2007 04:49:00 -0400 (EDT)
*References*: <f990ds$btq$1@smc.vnet.net>
Asim <maa48 at columbia.edu> 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.
David
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