Ramanujan's "Lost" notebook IX: the partial theta function as an entire function

被引：15
|
作者：
Andrews, GE [1 ]
机构：
[1] Penn State Univ, Number Theory Grp, Dept Math, University Pk, PA 16802 USA
来源：
ADVANCES IN MATHEMATICS | 2005年 / 191卷 / 02期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1016/j.aim.2004.03.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish the infinite product expansion for Sigma(ngreater than or equal to0) a(n) q(n2). This is a corrected version of the expansion stated in Ramanujan's "Lost" Notebook. The proof requires the study of a new family of polynomials which while not orthogonal have many similar properties. (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：408 / 422
页数：15
相关论文
共 50 条
  • [31] Elementary analysis in Ramanujan's lost notebook
    Hirschhorn, Michael D.
    RAMANUJAN JOURNAL, 2015, 37 (03): : 641 - 651
  • [32] Ramanujan’s ‘‘Lost Notebook’’ and the Virasoro Algebra
    A. Milas
    Communications in Mathematical Physics, 2004, 251 : 567 - 588
  • [33] Four identities related to third order mock theta functions in Ramanujan's lost notebook
    Yesilyurt, H
    ADVANCES IN MATHEMATICS, 2005, 190 (02) : 278 - 299
  • [34] "Algebraical oddities" in Ramanujan's lost notebook
    Hirschhorn, Michael D.
    RAMANUJAN JOURNAL, 2012, 29 (1-3): : 69 - 77
  • [35] ELEMENTARY ALGEBRA IN RAMANUJAN'S LOST NOTEBOOK
    Hirschhorn, Michael D.
    Sinescu, Vasile
    FIBONACCI QUARTERLY, 2013, 51 (02): : 123 - 129
  • [36] On sums of powers in Ramanujan's lost notebook
    Berndt, Bruce C.
    Schultz, Daniel
    APPLICABLE ANALYSIS, 2011, 90 (3-4) : 725 - 730
  • [37] Eisenstein series in Ramanujan's lost notebook
    Berndt, BC
    Chan, HH
    Sohn, J
    Son, SH
    RAMANUJAN JOURNAL, 2000, 4 (01): : 81 - 114
  • [38] Cranks and dissections in Ramanujan's lost notebook
    Berndt, BC
    Chan, HH
    Chan, SH
    Liaw, WC
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 2005, 109 (01) : 91 - 120
  • [39] Eisenstein Series in Ramanujan's Lost Notebook
    Bruce C. Berndt
    Heng Huat Chan
    Jaebum Sohn
    Seung Hwan Son
    The Ramanujan Journal, 2000, 4 : 81 - 114
  • [40] Ramanujan's "Lost Notebook" and the Virasoro algebra
    Milas, A
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 251 (03) : 567 - 588
12345