Vandermonde'S Identity

(Theory)

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Theory
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What is 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

Technology Types

factorial and binomial topicidentitymathematical identitypersonalitypropositionstatementtheoremtheorems in combinatorictheory

Synonyms

Chu-Vandermonde identityChu–Vandermonde identityVandemonde's formulaVandermonde convolutionVandermonde convolution formulaVandermonde identityVandermonde's convolution

Translations

Identidad de Vandermonde (es)Identidade de Vandermonde (pt)Identità di Vandermonde (it)Identiteit van Vandermonde (nl)Vandermondova konvoluce (cs)Тождество Вандермонда (ru)متطابقة فاندرموند (ar)范德蒙恒等式 (zh)

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