Multivariate q-Combinatorics and q-Hypergeometric Series

Multivariate q-hypergeometric series, which facilitate the study of multivariate discrete q-distributions, are presented in this chapter. Precisely, the notion of a q-multinomial coefficient of a real number, is introduced and two versions of a recurrence relation are obtained. Also, a q-combinatorial interpretation of the q-multinomial coefficient of a positive integer is provided.