On Ramanujan's cubic transformation formula for 2F1(1/3, 2/3; 1; z)

被引：29

作者：

Chan, HH ^{[1
]}

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 119260, Singapore

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 1998年 / 124卷

关键词：

D O I：

10.1017/S0305004198002643

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main aim of this paper is to provide two new proofs of Ramanujan's cubic transformation formula for F-2(1)(1/3, 2/3; 1; z) (see (1.8) below). For our first proof, we have to develop Ramanujan's elliptic functions in the theory of signature 3 using a different approach from that given in a recent paper by Berndt, Bhargava and Garvan. For our second proof, we use two of Goursat's formulas.

引用

页码：193 / 204

页数：12

共 13 条

[1]

[Anonymous], 1984, ENSEIGN MATH

[2]

Berndt B. C., 1989, Ramanujan's Notebooks

[3]

Berndt B. C., 1991, Ramanujan's Notebooks

[4]

BERNDT BC, RAMANUJAN MODULAR J

[5]

BERNDT BC, 1995, T AM MATH SOC, V347, P4136

[6] SOME CUBIC MODULAR IDENTITIES OF RAMANUJAN [J].

BORWEIN, JM ;

BORWEIN, PB ;

GARVAN, FG .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 343 (01) :35-47

[7] 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

[8]

CHAN HH, 1995, ACTA ARITH, V73, P343

[9]

COPSON ET, 1948, THEORY FUNCTIONS COM

[10]

Goursat E., 1881, ANN SCI ECOLE NORM S, V10, P3

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