English

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 s s , then the point z=s z=s 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

R2 v1 2026-06-23T14:17:16.285Z