Apéry Limits: Experiments and Proofs
نویسندگان
چکیده
An important component of Apéry’s proof that ζ(3) is irrational involves representing as the limit quotient two rational solutions to a three-term recurrence. We present various approaches such Apéry limits and highlight connections continued fractions well famous theorems Poincaré Perron on difference equations. In spirit Jon Borwein, we advertise an experimental mathematics approach by first exploring in detail simple but instructive motivating example. conclude with open problems.
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ژورنال
عنوان ژورنال: American Mathematical Monthly
سال: 2021
ISSN: ['1930-0972', '0002-9890']
DOI: https://doi.org/10.1080/00029890.2021.1962153