论文标题
$ e $的妄想和持续分数
Derangements and Continued Fractions for $e$
论文作者
论文摘要
$ e $的几个持续分数扩展是由称为\ emph {the ramanujan Machine}的自动猜想发生器（ACG）生产的。其中一些已经知道，有些最近已被证明，有些尚未得到证实。虽然ACG可以产生有趣的推定结果，但它对它们的意义提供了非常有限的见解。在本文中，我们使用阶乘与子分数或扰动数字的比率顺序得出了相当于Ramanujan机器结果的优雅持续分数扩展。
Several continued fraction expansions for $e$ have been produced by an automated conjecture generator (ACG) called \emph{The Ramanujan Machine}. Some of these were already known, some have recently been proved and some remain unproven. While an ACG can produce interesting putative results, it gives very limited insight into their significance. In this paper, we derive an elegant continued fraction expansion, equivalent to a result from the Ramanujan Machine, using the sequence of ratios of factorials to subfactorials or derangement numbers.
