1 research outputs found
On an Asymptotic Series of Ramanujan
An asymptotic series in Ramanujan's second notebook (Entry 10, Chapter 3) is
concerned with the behavior of the expected value of for large
where is a Poisson random variable with mean and
is a function satisfying certain growth conditions. We generalize this by
studying the asymptotics of the expected value of when the
distribution of 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.Comment: To appear, Ramanujan