Vandermonde's identity
Mathematical theorem on convolved binomial coefficients / From Wikipedia, the free encyclopedia
For the expression for a special determinant, see Vandermonde matrix.
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.[1]
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