ABEL'S METHOD ON SUMMATION BY PARTS FOR ELLIPTIC HYPERGEOMETRIC SERIES

被引：1

作者：

Chu, Wenchang ^{[2
]}

Jia, Cangzhi ^{[1
]}

机构：

[1] Northeast Univ, Dept Math, Shenyang 110005, Peoples R China

[2] Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2009年 / 11卷 / 03期

基金：

美国国家科学基金会;

关键词：

Abel's lemma on summation by parts; modified Jacobi theta function; elliptic (theta) hypergeometric series; Bailey's very-well-poised 10 phi 9-series transformation;

D O I：

10.1142/S0219199709003387

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By means of Abel's lemma on summation by parts, a new approach for evaluating elliptic hypergeometric series is presented. Some well-known terminating series identities are reviewed and several new transformation and summation formulae are established.

引用

页码：337 / 353

页数：17

共 50 条

[1] Abel's method on summation by parts and hypergeometric series
Wenchang, Chu
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2006, 12 (08) : 783 - 798
[2] Abel's method on summation by parts and theta hypergeometric series
Chu, Wenchang
Jia, Cangzhi
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2008, 115 (05) : 815 - 844
[3] Abel's lemma on summation by parts and basic hypergeometric series
Chu, Wenchang
ADVANCES IN APPLIED MATHEMATICS, 2007, 39 (04) : 490 - 514
[4] Abel's method on summation by parts and hypergeometric contiguous relations
Chu, Wenchang
Wang, Xiaoxia
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2007, 18 (11) : 771 - 807
[5] The modified Abel lemma on summation by parts and terminating hypergeometric series identities
Chu, Wenchang
Wang, Xiaoxia
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2009, 20 (02) : 93 - 118
[6] Abel’s method on summation by parts and nonterminatingq-series identities
Wenchang Chu
Wenlong Zhang
Collectanea mathematica, 2009, 60 : 193 - 211
[7] Abel's method on summation by parts and nonterminating q-series identities
Chu, Wenchang
Zhang, Wenlong
COLLECTANEA MATHEMATICA, 2009, 60 (02) : 193 - 211
[8] ABEL'S METHOD ON SUMMATION BY PARTS AND BALANCED q-SERIES IDENTITIES
Chu, Wenchang
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2010, 4 (01) : 54 - 65
[9] Summation formulae for elliptic hypergeometric series
Warnaar, SO
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (02) : 519 - 527
[10] Summation and transformation formulas for elliptic hypergeometric series
Warnaar, SO
CONSTRUCTIVE APPROXIMATION, 2002, 18 (04) : 479 - 502

← 1 2 3 4 5 →