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In Gelfand and Shilov Vol I (of Generalized Function), on page 257, they write down the following equation that I don't know how to arrive at:

$$\int_{0}^{1} (1-t)^{-\frac{n}{2}} t^{\frac{q-2}{2}}dt = \frac{\Gamma(\frac{q}{2})\Gamma(-n/2+1)}{\Gamma(-p/2+1)}\;,$$

where $p+q=n$.

How to arrive at this identity?

Thanks.

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1 Answer 1

up vote 1 down vote accepted

This is the expression of the Beta function in terms of the Gamma function, for $B(-n/2 + 1, q/2)$.

http://en.wikipedia.org/wiki/Beta_function

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