On an Asymptotic Series of Ramanujan
نویسنده
چکیده
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 binomial, negative binomial, and gamma families. Some formulas associated with the negative binomial appear new.
منابع مشابه
Asymptotic Expansion of a Series of Ramanujan
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تاریخ انتشار 2009