On the theory of elliptic functions based on 2F1(1/3, 2/3; 1/2; z)

被引：5

作者：

Shen, LC ^{[1
]}

机构：

[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 357卷 / 05期

关键词：

Jacobian elliptic functions; theta functions; Weierstrass p function;

D O I：

10.1090/S0002-9947-04-03600-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Based on properties of the hypergeometric series F-2(1)(1/3, 2/3; 1/2; z), we develop a theory of elliptic functions that shares many striking similarities with the classical Jacobian elliptic functions.

引用

页码：2043 / 2058

页数：16

共 5 条

[1] 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

[2]

Erdelyi A, 1953, HIGHER TRANSCENDENTA

[3] On an identity of Ramanujan based on the hypergeometric series 2F1(1/3,2/3; 1/2; x). [J].

Shen, LC .

JOURNAL OF NUMBER THEORY, 1998, 69 (02) :125-134

[4] ON THE MODULAR EQUATIONS OF DEGREE-3 [J].

SHEN, LC .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 122 (04) :1101-1114

[5]

Whittaker E.T., 1966, COURSE MODERN ANAL

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