A simple algorithm for expanding a power series as a continued fraction

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-06-01 DOI:10.1016/j.exmath.2022.12.001

Alan D. Sokal

引用次数: 6

Abstract

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).

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将幂级数展开为连分式的一个简单算法

我提出并讨论了一个极其简单的算法，用于将形式幂级数扩展为连续分数。这个算法可以追溯到Euler（1746）和Viscovatov（1805），值得大家更好地了解。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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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