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.