Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL
Preprint
Abstract
We give an overview of our formalizations in the proof assistant Isabelle/HOL of certain irrationality and transcendence criteria for infinite series from three different research papers: by Erd\H{o}s and Straus (1974), Han\v{c}l (2002), and Han\v{c}l and Rucki (2005). Our formalizations in Isabelle/HOL can be found on the Archive of Formal Proofs. Here we describe selected aspects of the formalization and discuss what this reveals about the use and potential of Isabelle/HOL in formalizing modern mathematical research, particularly in these parts of number theory and analysis.Keywords
All Related Versions
This publication has 9 references indexed in Scilit:
- Formalising Mathematics – in Praxis; A Mathematician’s First Experiences with Isabelle/HOL and the Why and How of Getting StartedJahresbericht der Deutschen Mathematiker-Vereinigung, 2020
- Hammering towards QED2016
- The Transcendence of Certain Infinite SeriesRocky Mountain Journal of Mathematics, 2005
- A Theorem on Transcendence of Infinite Series IIJournal of Number Theory, 2001
- A Theorem on Transcendence of Infinite SeriesRocky Mountain Journal of Mathematics, 2000
- Criterion for Irrational SequencesJournal of Number Theory, 1993
- The foundation of a generic theorem proverJournal of Automated Reasoning, 1989
- On the irrationality of certain seriesPacific Journal of Mathematics, 1974
- Rational approximations to algebraic numbersMathematika, 1955