Multinomial Series

A generalization of the Binomial Series discovered by Johann Bernoulli and Leibniz.

$$(a_1+a_2+\ldots+a_k)^n = \sum_{n_1, n_2, \ldots, n_k} {n!\over n_1!n_2!\cdots n_k!} {a_1}^{n_1}{a_2}^{n_2}\cdots {a_k}^{n_k},$$

where $n \equiv n_1+n_2+\ldots +n_k$. The multinomial series arises in a generalization of the Binomial Distribution called the Multinomial Distribution.

See also Binomial Series, Multinomial Distribution