Certain families of elliptic functions defined by q-series

被引：3

作者：

Kurokawa, N ^{[1
]}

Wakayama, M

机构：

[1] Tokyo Inst Technol, Dept Math, Tokyo 1520033, Japan

[2] Kyushu Univ, Fac Math, Hakozaki, Fukuoka 8128581, Japan

来源：

RAMANUJAN JOURNAL | 2005年 / 10卷 / 01期

基金：

日本学术振兴会;

关键词：

q-series; Weierstrass zeta-function; elliptic functions; Eisenstein series; algebraic differential equations; q-gamma function;

D O I：

10.1007/s11139-005-3503-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce certain families of elliptic functions involving the Weierstrass p-function via q-series systematically and investigate their analytic and algebraic properties. Especially, we give examples of non-linear algebraic ordinary differential equations satisfied by some such elliptic functions.

引用

页码：23 / 41

页数：19

共 50 条

[1] Certain Families of Elliptic Functions Defined by q-Series
Nobushige Kurokawa
Masato Wakayama
[J]. The Ramanujan Journal, 2005, 10 : 23 - 41
[2] Certain q-series identities
Agarwal, Praveen
Jain, Shilpi
Choi, Junesang
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2017, 111 (01) : 139 - 146
[3] Certain q-series identities
Praveen Agarwal
Shilpi Jain
Junesang Choi
[J]. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017, 111 : 139 - 146
[4] q-series identities and values of certain L-functions
Andrews, GE
Jiménez-Urroz, J
Ono, K
[J]. DUKE MATHEMATICAL JOURNAL, 2001, 108 (03) : 395 - 419
[5] On Arithmetical Properties of Certain q-Series
Ville Merilä
[J]. Results in Mathematics, 2009, 53 : 129 - 151
[6] On certain pairs of q-series identities
Pee Choon Toh
[J]. The Ramanujan Journal, 2016, 40 : 359 - 365
[7] Certain transformation formulae for q-series
Prakash, Satya
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, 2007, 77A : 347 - 351
[8] On certain pairs of q-series identities
Toh, Pee Choon
[J]. RAMANUJAN JOURNAL, 2016, 40 (02): : 359 - 365
[9] SUMS OF A CERTAIN CLASS OF Q-SERIES
SRIVASTAVA, HM
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1989, 65 (01) : 8 - 11
[10] On Arithmetical Properties of Certain q-Series
Merila, Ville
[J]. RESULTS IN MATHEMATICS, 2009, 53 (1-2) : 129 - 151

← 1 2 3 4 5 →