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

Famous quotes containing the word identity:

    “One of the most highly valued functions of used parents these days is to be the villains of their children’s lives, the people the child blames for any shortcomings or disappointments. But if your identity comes from your parents’ failings, then you remain forever a member of the child generation, stuck and unable to move on to an adulthood in which you identify yourself in terms of what you do, not what has been done to you.”
    —Frank Pittman (20th century)