On Ramanujan's function k(q)=r(q)r 2(q 2)

被引：21

作者：

Cooper, Shaun ^{[1
]}

机构：

[1] Massey Univ Albany, IIMS, N Shore Mail Ctr, Auckland, New Zealand

来源：

RAMANUJAN JOURNAL | 2009年 / 20卷 / 03期

关键词：

Atkin-Lehner involution; Eisenstein series; Eta-function; Ramanujan's lost notebook; Ramanujan's second notebook; Rogers-Ramanujan continued fraction; Theta function; INFINITE PRODUCT IDENTITIES; CONTINUED-FRACTION; MODULAR EQUATIONS; SERIES; FORMULAS;

D O I：

10.1007/s11139-009-9198-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In both his second and lost notebooks, Ramanujan introduced a function, related to the Rogers-Ramanujan continued fraction and its quadratic transformation, and listed several of its properties. We extend these results and develop a systematic theory.

引用

页码：311 / 328

页数：18

共 25 条

[1] Andrews G.E., 2005, Ramanujan's Lost Notebook
[2] [Anonymous], 1988, LOST NOTEBOOK OTHER
[3] Berndt B.C., 1991, Ramanujans Notebooks: Part I
[4] Berndt B.C., 2006, Number Theory in the Spirit of Ramanujan
[5] BERNDT BC, 1998, RAMANUJANS NOTEBOO 5
[6] BLECKSMITH R, 1988, MATH COMPUT, V51, P301, DOI 10.1090/S0025-5718-1988-0942157-2
[7] Triple product identity, quintuple product identity and Ramanujan's differential equations for the classical Eisenstein series
Chan, Heng Huat
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (07) : 1987 - 1992
[8] Chan HH, 2009, MATH RES LETT, V16, P405
[9] On the equivalence of Ramanujan's partition identities and a connection with the Rogers-Ramanujan continued fraction
Chan, HH
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 198 (01) : 111 - 120
[10] Ramanujan's modular equations and Atkin-Lehner involutions
Chan, HH
Lang, ML
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1998, 103 (1) : 1 - 16

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