Articles containing proofs | Mathematical identities | Factorial and binomial topics

Vandermonde's identity

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. There is a q-analog to this theorem called the q-Vandermonde identity. Vandermonde's identity can be generalized in numerous ways, including to the identity (Wikipedia).

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Related pages

Double counting (proof technique) | Hockey-stick identity | Hypergeometric distribution | Rothe–Hagen identity | Q-analog | Polynomial | Hypergeometric function | Umbral calculus | Combinatorics | Binomial series | Alexandre-Théophile Vandermonde | Cauchy product | Binomial type | Binomial theorem | Gamma function | Binomial coefficient | Integer | Q-Vandermonde identity | Probability distribution | Subset | Complex number