论文标题
Apéry限制：实验和证明
Apéry Limits: Experiments and Proofs
论文作者
论文摘要
Apéry证明$ζ（3）$的重要组成部分是不合理的，涉及代表$ζ（3）$作为两种理性解决方案商的限制到三届复发。我们介绍了这种Apéry限制的各种方法，并突出了与持续分数以及Poincaré和Perron在差异方程式上的著名定理的联系。本着乔恩·博韦（Jon Borwein）的精神，我们首先详细探讨一个简单但有启发性的激励榜样，宣传了一种实验数学方法。我们以各种开放问题结束。
An important component of Apéry's proof that $ζ(3)$ is irrational involves representing $ζ(3)$ as the limit of the quotient of two rational solutions to a three-term recurrence. We present various approaches to such Apéry limits and highlight connections to continued fractions as well as the famous theorems of Poincaré and Perron on difference equations. In the spirit of Jon Borwein, we advertise an experimental-mathematics approach by first exploring in detail a simple but instructive motivating example. We conclude with various open problems.
