ALGEBRAIC STATEMENTS SIMILAR TO THOSE IN RAMANUJAN'S "LOST NOTEBOOK"

被引：0
|
作者：
Cooper, Curtis [1 ]
机构：
[1] Univ Cent Missouri, Dept Math & Comp Sci, Warrensburg, MO 64093 USA
来源：
FIBONACCI QUARTERLY | 2014年 / 52卷 / 05期
关键词：
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Ramanujan's "lost notebook" contains algebraic statements if g(4) = 5, then (5)root 3+2g - (5)root 4-4g/(5)root 3+2g + (5)root 4-4g =2 + g + g(2) + g(3), and if g(5) = 2, then root 1+g(2) = g(4) +g(3)+g-1/root 5 In this paper we will discover algebraic statements similar to those in Ramanujan's "lost notebook". For example, we will prove algebraic statements like if g(3) = 2, then (4)root 111-87g + (4)root g-1/(4)root 111-87g - (4)root g-1 = 2+g+g(2), and if g(5) = 2, then root-3g(2)+4g+5 = g(4)+g+1.
引用
收藏
页码：91 / 101
页数：11
相关论文
共 50 条
  • [1] Simplicity and surprise in Ramanujan's ''lost'' notebook
    Andrews, GE
    AMERICAN MATHEMATICAL MONTHLY, 1997, 104 (10): : 918 - 925
  • [2] Elementary analysis in Ramanujan’s lost notebook
    Michael D. Hirschhorn
    The Ramanujan Journal, 2015, 37 : 641 - 651
  • [3] Some integrals in Ramanujan's lost notebook
    Berndt, BC
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (10) : 2983 - 2988
  • [4] “Algebraical oddities” in Ramanujan’s lost notebook
    Michael D. Hirschhorn
    The Ramanujan Journal, 2012, 29 : 69 - 77
  • [5] EULER PRODUCTS IN RAMANUJAN'S LOST NOTEBOOK
    Berndt, Bruce C.
    Kim, Byungchan
    Williams, Kenneth S.
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2013, 9 (05) : 1313 - 1349
  • [6] Elementary analysis in Ramanujan's lost notebook
    Hirschhorn, Michael D.
    RAMANUJAN JOURNAL, 2015, 37 (03): : 641 - 651
  • [7] Ramanujan’s ‘‘Lost Notebook’’ and the Virasoro Algebra
    A. Milas
    Communications in Mathematical Physics, 2004, 251 : 567 - 588
  • [8] "Algebraical oddities" in Ramanujan's lost notebook
    Hirschhorn, Michael D.
    RAMANUJAN JOURNAL, 2012, 29 (1-3): : 69 - 77
  • [9] ELEMENTARY ALGEBRA IN RAMANUJAN'S LOST NOTEBOOK
    Hirschhorn, Michael D.
    Sinescu, Vasile
    FIBONACCI QUARTERLY, 2013, 51 (02): : 123 - 129
  • [10] On sums of powers in Ramanujan's lost notebook
    Berndt, Bruce C.
    Schultz, Daniel
    APPLICABLE ANALYSIS, 2011, 90 (3-4) : 725 - 730
12345