Hello. Who can help me to prove the following? $\displaystyle B(p,q) = \displaystyle\frac{q-1}{p}B(p+1,q-1)= \displaystyle\frac{p-1}{q}B(p-1,q-1)$ $\displaystyle p,q > 1 $ Thanks
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You know $\displaystyle \beta(a,b)=\frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}$ and $\displaystyle \Gamma(1+a)=a\Gamma(a)$ so use those identities to establish your expression.
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