A note for alternating Ramanujan's circular summation formula

被引：3
作者：
Liu, Xian-Fang [1 ]
Luo, Qiu-Ming [1 ]
机构：
[1] Chongqing Normal Univ, Dept Math, Chongqing Higher Educ Mega Ctr, Huxi Campus, Chongqing 401331, Peoples R China
来源：
FORUM MATHEMATICUM | 2015年 / 27卷 / 06期
关键词：
Elliptic functions; alternating circular summation; theta functions; theta function identities; THETA-FUNCTIONS; MODULAR EQUATIONS; LOST NOTEBOOK; POWERS; IDENTITY;
D O I：
10.1515/forum-2013-0148
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, Zhu gave an alternating circular summation of theta functions (see [26]). In this paper, we further extend Zhu's results. Some applications are also shown.
引用
收藏
页码：3189 / 3203
页数：15
相关论文
共 26 条
  • [1] The sixth, eighth, ninth, and tenth powers of Ramanujan's theta function
    Ahlgren, S
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (05) : 1333 - 1338
  • [2] [Anonymous], 2012, RAMANUJANS LOST NO 3
  • [3] Bellman R., 1961, A brief introduction to theta functions
  • [4] Berndt B.C, 1998, RAMANUJANS NOTEBOO 5
  • [5] Berndt B. C., 1991, Ramanujan's Notebooks
  • [6] ADDITIVE DECOMPOSITIONS OF THETA-FUNCTIONS OF MULTIPLE ARGUMENTS
    BOON, M
    GLASSER, ML
    ZAK, J
    ZUCKER, IJ
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1982, 15 (11): : 3439 - 3440
  • [7] A CUBIC COUNTERPART OF JACOBIS IDENTITY AND THE AGM
    BORWEIN, JM
    BORWEIN, PB
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 323 (02) : 691 - 701
  • [8] Some circular summation formulas for theta functions
    Cai, Yi
    Chen, Si
    Luo, Qiu-Ming
    [J]. BOUNDARY VALUE PROBLEMS, 2013,
  • [9] Circular summation of theta functions in Ramanujan's Lost Notebook
    Chan, HH
    Liu, ZG
    Ng, ST
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 316 (02) : 628 - 641
  • [10] On a new circular summation of theta functions
    Chan, Song Heng
    Liu, Zhi-Guo
    [J]. JOURNAL OF NUMBER THEORY, 2010, 130 (05) : 1190 - 1196
123