华东师范大学学报（自然科学版） >

2015 , Vol. 2015 >Issue 6: 46 - 52

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.06.007

应用数学与基础数学

关于一个三次q-级数部分和的新变换(英)

  • 王琛颖
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  • 南京信息工程大学~~数学与统计学院, 南京 210044
王琛颖, 女, 讲师, 博士, 研究方向为组合分析.

收稿日期: 2015-04-24

  网络出版日期: 2015-12-23

基金资助

国家自然科学基金数学天元基金(11226278)

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New transformation for the partial sum of a cubic q-series

  • WANG Chen-Ying
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Received date: 2015-04-24

  Online published: 2015-12-23

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摘要

利用Abel分部求和引理研究了一个三次基本超几何级数部分和,建立了一个关于这个 三次级数的新的变换公式.
此变换推广了几个已知的三次q-级数求和公式.

关键词： 基本超几何级数; Abel分部求和引理; 三次q-级数变换

本文引用格式

王琛颖 . 关于一个三次q-级数部分和的新变换(英)[J]. 华东师范大学学报（自然科学版）, 2015 , 2015(6) : 46 -52 . DOI: 10.3969/j.issn.1000-5641.2015.06.007

Abstract

The partial sum of a cubic basic hypergeometric series is investigated by means of the modified Abel's lemma on summation by
parts. A new transformation formula for the cubic series is established, which expands some known cubic q-series summation
formulae.

参考文献

[1]CHU W, WANG C. Abel's lemma on summation by parts and partialq-series transformations [J]. Science in China Ser A, 2009, 52(4):720-748.
[2] GASPER G, RAHMAN M.Basic Hypergeometric Series [M]. Cambridge: Cambridge University Press, 2004.
[3] SLATER L J.Generalized Hypergeometric Functions [M]. Cambridge: CambridgeUniversity Press, 1966.
[4] CHU W.Inversion techniques and combinatorial identities [J]. Bollettino UM I, 1993(7): 737-760.
[5] CHU W.Inversion techniques and combinatorial identities: Jackson's $q$-analogue of the Dougall-Dixon theorem and the dual formulae [J].Compositio Mathematica, 1995, 95(1): 43-68.
[6] GASPER G.Summation, transformation, and expansion formulas for bibasic series[J]. Trans Amer Math Soc, 1989, 312(1): 257-277.
[7] GASPER G, RAHMAN M.An indefinite bibasic summation formula and some quadratic, cubic and quartic summation and transformation formulas [J].Can J Math 1990, 42: 1-27.
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