From: Cris Moore <moore@santafe.edu>
Subject: Re: generating functions & power laws
Date: Wed, 19 Jan 2000 17:28:04 -0700
Newsgroups: sci.math.research
Summary: [missing]

I wrote:

> My coauthor and I have re-proved that if the coefficients of a generating
> function H(z) = \sum_i n_i z^i decay as a power law, n_i ~ i^(-a) for some
> exponent a, then H(z) will have an algebraic singularity at z=1 of the
> form H(1-eps) ~ eps^(a-1), at least when 1 < a < 2.

with the help of Philippe Flajolet and others, I have learned that this
is the Tauberian theorem of Littlewood and Hardy.

Thanks again to the readers of this newsgroup for your help...

- Cris