Engel expansions and the Rogers-Ramanujan identities

被引：11

作者：

Andrews, GE ^{[1
]}

Knopfmacher, A

Knopfmacher, J

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Univ Witwatersrand, Dept Computat & Appl Math, ZA-2050 Wits, South Africa

[3] Univ Witwatersrand, Dept Math, Ctr Applicable Anal & Number Theory, ZA-2050 Wits, South Africa

来源：

JOURNAL OF NUMBER THEORY | 2000年 / 80卷 / 02期

基金：

美国国家科学基金会;

关键词：

Engel expansions; Rogers-Ramanujan identities; acceleration of convergence;

D O I：

10.1006/jnth.1999.2453

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the previously developed extension of the Engel expansion to the field of Formal Laurent series. We examine three separate aspects. First we consider the algorithm in relation to the work of Ramanujan. Second we show how the algorithm can be used to prove expansions such as those found by Euler, Rogers, and Ramanujan. Finally we remark briefly on its use in acceleration of convergence. (C) 2000 Academic Press.

引用

页码：273 / 290

页数：18