





















An asymptotic series in Ramanujan's second notebook (Entry 10, Chapter 3) is concerned with the behavior of the expected value of $φ(X)$ for large $λ$ where $X$ is a Poisson random variable with mean $λ$ and $φ$ is a function satisfying certain growth conditions. We generalize this by studying the asymptotics of the expected value of $φ(X)$ when the distribution of $X$ belongs to a suitable family indexed by a convolution parameter. Examples include the problem of inverse moments for distribution families such as the binomial or the negative binomial.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。