RAMANUJAN'S CUBIC CONTINUED FRACTION AND AN ANALOG OF HIS "MOST BEAUTIFUL IDENTITY"

被引：97

作者：

Chan, Hei-Chi ^{[1
]}

机构：

[1] Univ Illinois, Dept Math Sci, Springfield, IL 62703 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2010年 / 6卷 / 03期

关键词：

Ramanujan's cubic continued fraction; Ramanujan's "Most Beautiful Identity; EXPLICIT EVALUATIONS;

D O I：

10.1142/S1793042110003150

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove an analog of Ramanujan's "Most Beautiful Identity". This analog is closely related to Ramanujan's beautiful results involving the cubic continued fraction.

引用

页码：673 / 680

页数：8

共 50 条

[21] On the Expansion of Ramanujan's Continued Fraction
Michael D. Hirschhorn
The Ramanujan Journal, 1998, 2 : 521 - 527
[22] On the expansion of Ramanujan's continued fraction
Hirschhorn, MD
RAMANUJAN JOURNAL, 1998, 2 (04): : 521 - 527
[23] FROM A RAMANUJAN-SELBERG CONTINUED FRACTION TO A JACOBIAN IDENTITY
Chan, Hei-Chi
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (09) : 2849 - 2856
[24] Ramanujan's Continued Fraction, a Generalization and Partitions
Srivastava, Bhaskar
KYUNGPOOK MATHEMATICAL JOURNAL, 2005, 45 (02): : 273 - 280
[25] Modular curves and Ramanujan's continued fraction
Cais, Bryden
Conrad, Brian
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2006, 597 : 27 - 104
[26] An entry of Ramanujan on continued fraction involving the gamma function in his notebooks
Jo, Sihun
JOURNAL OF NUMBER THEORY, 2012, 132 (12) : 2947 - 2954
[27] The Rogers-Ramanujan continued fraction and a new Eisenstein series identity
Chan, Heng Huat
Chan, Song Heng
Liu, Zhi-Guo
JOURNAL OF NUMBER THEORY, 2009, 129 (07) : 1786 - 1797
[28] A continued fraction from Ramanujan's lost notebook
Berndt B.C.
Choi G.
aequationes mathematicae, 2005, 69 (3) : 257 - 262
[29] An idea on some of Ramanujan’s continued fraction identities
Lisa Lorentzen
The Ramanujan Journal, 2008, 17 : 369 - 385
[30] An idea on some of Ramanujan's continued fraction identities
Lorentzen, Lisa
RAMANUJAN JOURNAL, 2008, 17 (03): : 369 - 385

← 1 2 3 4 5 →