Asymptotic Normality of the \((r,\beta)\)-Stirling Numbers

Abstract

In this paper, the unimodality of \((r,\beta)\)-Stirling numbers and certain asymptotic approximation of \((r,\beta)\)-Bell numbers are established. Together with these results and the most general form of Central Limit Theorem, viz. Bounded Variance Normal Convergence Criterion, the \((r,\beta)\)-Stirling numbers are shown to be asymptotically normal.