From: Cris Moore 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