In combinatorics, Vandermonde's identity (or Vandermonde's convolution) is the following identity for binomial coefficients:
for any nonnegative integers r, m, n. The identity is named after Alexandre-Théophile Vandermonde (1772), although it was already known 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.
Vandermonde's identity can be generalized in numerous way...