In this work we establish local limit theorems for q-multinomial and multiple Heine distributions. Specifically, the pointwise convergence of the q-multinomial distribution of the first kind, as well as for its discrete limit, the multiple Heine distribution, to a multivariate Stieltjes-Wigert type distribution, are provided.

翻译：本文建立了$q$-多项分布与多重海涅分布的中心极限定理。具体而言，我们证明了第一类$q$-多项分布及其离散极限——多重海涅分布，均逐点收敛于多元Stieltjes-Wigert型分布。