The Rogers-Ramanujan continued fraction and its level 13 analogue

被引：13
|
作者：
Cooper, Shaun [1 ]
Ye, Dongxi [1 ]
机构：
[1] Massey Univ Albany, North Shore Mail Ctr, Inst Nat & Math Sci, Auckland, New Zealand
来源：
JOURNAL OF APPROXIMATION THEORY | 2015年 / 193卷
关键词：
Dedekind eta function; Eisenstein series; Hypergeometric function; Modular form; Pi; Ramanujan's theories of elliptic functions to alternative bases; ELLIPTIC FUNCTIONS; MODULAR-FUNCTIONS; SERIES; 1/PI;
D O I：
10.1016/j.jat.2014.01.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
One of the properties of the Rogers-Ramanujan continued fraction is its representation as an infinite product given by i(q) = q(1/5) Pi(infinity)(j=1) (1 - q(j))((j/5)) where (j/p) is the Legendre symbol. In this work we study the level 13 function R(q) = q Pi(infinity)(j=1) (1 - q(j))((j/13)) and establish many properties analogous to those for the fifth power of the Rogers-Ramanujan continued fraction. Many of the properties extend to other levels l for which l - 1 divides 24, and a brief account of these results is included. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：99 / 127
页数：29
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