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/).
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页码：245 / 287
页数：43
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