Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?


share|cite|improve this question
up vote 1 down vote accepted

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.