On Fabry’s Quotient Theorem

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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, then the point (Formula presented.) is a singular point of the series. This proof only uses material from undergraduate university studies.

Original languageEnglish
Pages (from-to)344-351
Number of pages8
JournalAmerican Mathematical Monthly
Issue number4
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics


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