Vandermonde's Identity - Generalized Vandermonde's Identity

Generalized Vandermonde's Identity

If in the algebraic derivation above more than two polynomials are used, it results in the generalized Vandermonde's identity. For y + 1 polynomials:

$\sum_{k_1+\dots +k_y = 0}^x {n\choose k_1} {n\choose k_2} {n\choose k_3} \cdots {n \choose x - \sum_{j = 1}^y k_j } = { \left( y + 1 \right) n \choose x}.$

Read more about this topic: Vandermonde's Identity

Famous quotes containing the words generalized and/or identity:

“One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.”
—H.L. (Henry Lewis)

“I look for the new Teacher that shall follow so far those shining laws that he shall see them come full circle; shall see their rounding complete grace; shall see the world to be the mirror of the soul; shall see the identity of the law of gravitation with purity of the heart; and shall show that the Ought, that Duty, is one thing with Science, with Beauty, and with Joy.”
—Ralph Waldo Emerson (1803–1882)