SOME CUBIC MODULAR IDENTITIES OF RAMANUJAN

被引：113

作者：

BORWEIN, JM ^{[1
]}

BORWEIN, PB ^{[1
]}

GARVAN, FG ^{[1
]}

机构：

[1] DALHOUSIE UNIV,DEPT MATH STAT & COMP SCI,HALIFAX B3H 3J5,NS,CANADA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 343卷 / 01期

关键词：

THETA FUNCTIONS; Q-SERIES; ETA FUNCTION; MODULAR FORMS; CUBIC MODULAR EQUATIONS; HYPERGEOMETRIC FUNCTIONS;

D O I：

10.2307/2154520

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

There is a beautiful cubic analogue of Jacobi's fundamental theta function identity: theta3(4) = theta4(4) + theta2(4) It is [GRAPHICS] Here omega = exp(2pii/3). In this note we provide an elementary proof of this identity and of a related identity due to Ramanujan. We also indicate how to discover and prove such identities symbolically.

引用

页码：35 / 47

页数：13

共 14 条

[1]

Andrews G. E., 1976, ENCY MATH APPL, V2

[2]

Bellman R., 1961, BRIEF INTRO THETA FU

[3]

Berndt B. C., 1991, RAMANUJANS NOTEBOOKS

[4]

Borwein J. M., 1987, PI AGM STUDY ANAL NU

[5] A CUBIC COUNTERPART OF JACOBIS IDENTITY AND THE AGM [J].

BORWEIN, JM ;

BORWEIN, PB .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 323 (02) :691-701

[6]

BORWEIN JM, 1990, LECTURE NOTES MATH, V1435

[7]

EWELL JA, 1986, FIBONACCI Q, V24, P151

[8]

Fine N. J., 1988, MATH SURVEYS MONOGRA, V27

[9]

KOLBERG O, 1959, NOTE EISENSTEIN SERI

[10]

KOLITSCH LW, 1990, P C HONOR PT BATEMAN

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