Q-Vandermonde Identity

Q-Vandermonde Identity

In mathematics, in the field of combinatorics, the q-Vandermonde identity is a q-analogue of the Chu-Vandermonde identity. Using standard notation for q-binomial coefficients, the identity states that

\binom{m + n}{k}_{\!\!q} = \sum_{j} \binom{m}{k - j}_{\!\!q} \binom{n}{j}_{\!\!q} q^{j(m-k+j)}.

(The nonzero contributions to this sum come from values of j such that the q-binomial coefficients on the right side are nonzero, that is, .)

Read more about Q-Vandermonde Identity:  Other Conventions, Proofs of The Identity

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