In combinatorics, Vandermonde's identity, or Vandermonde's convolution, named after Alexandre-Théophile Vandermonde (1772), states that
for binomial coefficients. 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.
Read more about Vandermonde's Identity: Algebraic Proof, Combinatorial Proof, Generalized Vandermonde's Identity, The Hypergeometric Probability Distribution, Chu–Vandermonde Identity
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“Let it be an alliance of two large, formidable natures, mutually beheld, mutually feared, before yet they recognize the deep identity which beneath these disparities unites them.”
—Ralph Waldo Emerson (1803–1882)