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
Famous quotes containing the word identity:
“One of the most highly valued functions of used parents these days is to be the villains of their children’s lives, the people the child blames for any shortcomings or disappointments. But if your identity comes from your parents’ failings, then you remain forever a member of the child generation, stuck and unable to move on to an adulthood in which you identify yourself in terms of what you do, not what has been done to you.”
—Frank Pittman (20th century)