THE ROGERS-RAMANUJAN CONTINUED FRACTION AND RELATED ETA-QUOTIENT REPRESENTATIONS

被引:13
作者
Chern, Shane [1 ]
Tang, Dazhao [2 ]
机构
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
[2] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China
关键词
Rogers– Ramanujan continued fraction; eta-quotient representations; recurrence relations;
D O I
10.1017/S0004972720000933
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We construct eta-quotient representations of two families of q-series involving the Rogers-Ramanujan continued fraction by establishing related recurrence relations. We also display how these eta-quotient representations can be utilised to dissect certain q-series identities.
引用
收藏
页码:248 / 259
页数:12
相关论文
共 21 条
[1]  
Andrews G.E, 2005, RAMANUJANS LOST NOTE
[2]  
ANDREWS GE, 1992, MEM AM MATH SOC, V99, pR3
[3]  
APOSTOL T, 1976, GRADUATE TEXTS MATH, V41
[4]  
Baruah N. D., ARXIV200506799
[5]   Exact generating functions for the number of partitions into distinct parts [J].
Baruah, Nayandeep Deka ;
Begum, Nilufar Mana .
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (07) :1995-2011
[6]  
Berndt B. C., 2004, NUMBER THEORY SPIRIT
[7]  
Chern S, IN PRESS
[8]  
Chern S, ARXIV180701890
[9]  
Cooper S., 2017, Ramanujan's Theta Functions
[10]   Modular equations for cubes of the Rogers-Ramanujan and Ramanujan-Gollnitz-Gordon functions and their associated continued fractions [J].
Gugg, Chadwick .
JOURNAL OF NUMBER THEORY, 2012, 132 (07) :1519-1553