Chu-Vandermonde Identity/Extended

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Theorem

Let $r, s, \alpha, \beta \in \C$ be complex numbers.


Then:

$\displaystyle \sum_{k \mathop \in \Z} \dbinom r {\alpha + k} \dbinom s {\beta - k}$

where $\dbinom r {\alpha + k}$ denotes a binomial coefficient.


Proof


Sources