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A local limit theorem for generalized Stirling numbers. (English) Zbl 0727.60024
Authors’ summary: We consider triangular arrays $S\sp n\sb k(a)$ of reals defined by the inversion $x\sp n=\sum\sp{n}\sb{k=0}S\sp n\sb k(a)(x-a\sb 0)\cdots (x-a\sb k),$ $n=0,1,\dots$, and establish the local limit theorem in case $a\sb 0,a\sb 1,\dots$ is an arithmetic progression. Additionally, the numbers $\sum\sp{n}\sb{k=0}S\sp n\sb k(a)$ are asymptotically evaluated. For a geometric progression $a\sb 0,a\sb 1,\dots$ not even a central limit theorem does hold.

60F05Central limit and other weak theorems
11B73Bell and Stirling numbers