I present and discuss an extremely simple algorithm for expanding a formal power series as a continued fraction. This algorithm, which goes back to Euler (1746) and Viscovatov (1805), deserves to be better known. I also discuss the connection of this algorithm with the work of Gauss (1812), Stieltjes (1889), Rogers (1907) and Ramanujan, and a combinatorial interpretation based on the work of Flajolet (1980).

中文翻译：

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将幂级数展开为连分数的简单算法

我提出并讨论了一种极其简单的算法，用于将形式幂级数展开为连续分数。这个算法可以追溯到 Euler (1746) 和 Viscovatov (1805)，值得更多人了解。我还讨论了该算法与 Gauss (1812)、Stieltjes (1889)、Rogers (1907) 和 Ramanujan 的工作的联系，以及基于 Flajolet (1980) 工作的组合解释。