On the expansion of Ramanujan's continued fraction

被引：22
|
作者：
Hirschhorn, MD [1 ]
机构：
[1] Univ New S Wales, Sch Math, Sydney, NSW 2052, Australia
来源：
RAMANUJAN JOURNAL | 1998年 / 2卷 / 04期
关键词：
Ramanujan's continued fraction; quintuple product identity;
D O I：
10.1023/A:1009789012006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
If Ramanujan's continued fraction (or its reciprocal) is expanded as a power series, the sign of the coefficients is (eventually) periodic with period 5. We give combinatorial interpretations for the coefficients from which the result is immediate. We make use of the quintuple product identity, which we prove.
引用
收藏
页码：521 / 527
页数：7
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