Vandermonde's Identity
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High Quality Content by WIKIPEDIA articles! In combinatorial mathematics, Vandermonde's identity, named after Alexandre-Théophile Vandermonde (1772), states that the equality {m+n choose r}=sum_{k=0}^r{m choose k}{n choose r-k},qquad m,n,rinmathbb{N}_0, for binomial coefficients holds. This identity was given already in 1303 by the Chinese mathematician Zhu Shijie (Chu Shi-Chieh). See Askey 1975, pp. 59-60 for the history. There is a q-analog to this theorem called the q-Vandermonde identity.

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High Quality Content by WIKIPEDIA articles! In combinatorial mathematics, Vandermonde's identity, named after Alexandre-Théophile Vandermonde (1772), states that the equality {m+n choose r}=sum_{k=0}^r{m choose k}{n choose r-k},qquad m,n,rinmathbb{N}_0, for binomial coefficients holds. This identity was given already in 1303 by the Chinese mathematician Zhu Shijie (Chu Shi-Chieh). See Askey 1975, pp. 59-60 for the history. There is a q-analog to this theorem called the q-Vandermonde identity.