alternate integral representation of beta function (2)


Substitute x:=11+s, dx=-1(1+s)2ds:

01xp-1(1-x)q-1𝑑x =01(1+s)p+1(s1+s)q-1𝑑s
=0sq-1(1+s)p+q𝑑s

Since B(p,q)=B(q,p) this gives:

0sp-1(1+s)p+q𝑑s =Γ(p)Γ(q)Γ(p+q)
Title alternate integral representation of beta function (2)
Canonical name AlternateIntegralRepresentationOfBetaFunction2
Date of creation 2013-03-22 18:34:31
Last modified on 2013-03-22 18:34:31
Owner karstenb (16623)
Last modified by karstenb (16623)
Numerical id 8
Author karstenb (16623)
Entry type Result
Classification msc 33B15