Irrational Rapidly Convergent Series

Angeliki Koutsoukou-Argyraki and Wenda Li

23 May 2018

Abstract

We formalize with Isabelle/HOL a proof of a theorem by J. Hancl asserting the irrationality of the sum of a series consisting of rational numbers, built up by sequences that fulfill certain properties. Even though the criterion is a number theoretic result, the proof makes use only of analytical arguments. We also formalize a corollary of the theorem for a specific series fulfilling the assumptions of the theorem.
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@article{Irrationality_J_Hancl-AFP,
  author  = {Angeliki Koutsoukou-Argyraki and Wenda Li},
  title   = {Irrational Rapidly Convergent Series},
  journal = {Archive of Formal Proofs},
  month   = May,
  year    = 2018,
  note    = {\url{http://isa-afp.org/entries/Irrationality_J_Hancl.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
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