### 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.

### License

BSD License

### Topics

- Mathematics/Number theory
- Mathematics/Analysis

### Session Irrationality_J_Hancl

- Irrationality_J_Hancl

## Cite

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Irrationality_J_Hancl-AFP

    @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{https://isa-afp.org/entries/Irrationality_J_Hancl.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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