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Chu vandermonde identity states that ${s+t \choose n}=\sum_{k=0}^n {s \choose k}{t \choose n-k} $

Now how to prove that this identity is a discrete form of beta integral?

i see as a starting point to rewrite this identity for n+1 by replacing n by n+1 , then what? any help? since after writing that i seem to be getting a very crude expression that leads me no where.

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Did you try rewriting the identity using beta functions? –  Sasha Aug 27 '11 at 14:05
    
for writing that i need to know the beta form of chu inequality here which i dont have, any further help ? –  Bhargav Aug 27 '11 at 14:38
    
This might be useful: $Beta(1+k, 1+n-k) = \frac{1}{n+1} \frac{1}{\binom{n}{k}}$ –  Sasha Aug 27 '11 at 14:59
1  
Do you want to find $p,q$ such that $\dbinom{s+t}{n}$ is expressed in terms of $B(p,q)$? –  Américo Tavares Aug 27 '11 at 15:46
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