On Fabry's quotient theorem
Complex Variables
2020-04-16 v2
Abstract
We present a short proof of the Fabry quotient theorem, which states that for a complex power series with unit radius of convergence, if the quotient of its consecutive coefficients tends to , then the point is a singular point of the series. This proof only uses material from undergraduate university studies.
Cite
@article{arxiv.2003.07661,
title = {On Fabry's quotient theorem},
author = {Lev Buhovsky},
journal= {arXiv preprint arXiv:2003.07661},
year = {2020}
}
Comments
8 pages. Proofs were slightly simplified, new references were added