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

被引：3

作者：

Sokal, Alan D. ^{[1
,2
]}

机构：

[1] UCL, Dept Math, London WC1E 6BT, England

[2] NYU, Dept Phys, 726 Broadway, New York, NY 10003 USA

来源：

EXPOSITIONES MATHEMATICAE | 2023年 / 41卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Formal power series; Continued fraction; Euler-Viscovatov algorithm; Gauss's continued fraction; Euler-Gauss recurrence method; Motzkin path; Dyck path; Stieltjes table; Rogers' addition formula; HYPERGEOMETRIC-SERIES; ELLIPTIC FUNCTIONS; PROOF;

D O I：

10.1016/j.exmath.2022.12.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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).& COPY; 2022 The Author(s). Published by Elsevier GmbH. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页码：245 / 287

页数：43

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