New contiguous relations for a balanced q-series and their applications

被引：0
作者：
Chenying Wang
Jianan Xu
机构：
[1] Nanjing University of Information Science and Technology,School of Mathematics and Statistics
[2] Nanjing University of Information Science and Technology,Center for Applied Mathematics of Jiangsu Province
[3] Nanjing University of Information Science and Technology,Jiangsu International Joint Laboratory on System Modeling and Data Analysis
[4] Soochow University,Department of Mathematics
来源：
The Ramanujan Journal | 2024年 / 64卷
关键词：
Basic hypergeometric series; Abel’s lemma on summation by parts; -Contiguous relation; Iteration; Rogers–Ramanujan type identity; Partial theta function; Transformation; Primary 33D15; Secondary 40G10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The present paper is mainly concerned with a balanced partial q-series. By the classical Abel lemma on summation by parts, we establish the q-contiguous relations for the partial sum whose iterating cases embrace many new summation and transformation formulae as well as some known results. Of particular interest are one identity of Rogers–Ramanujan type and two identities of partial theta functions.
引用
收藏
页码：275 / 287
页数：12
相关论文
共 10 条
  • [1] Chen X(2017)Summation formulae for a class of terminating balanced J. Math. Anal. Appl. 451 508-523
  • [2] Chu W(2006)-series J. Comb. Theory Ser. A 113 966-979
  • [3] Chu W (2007)Bailey’s very well-poised Adv. Appl. Math. 39 490-514
  • [4] Chu W (2009)-series identity Adv. Appl. Math. 42 358-391
  • [5] Chu W(2003)Abel’s lemma on summation by parts and basic hypergeometric series Trans. Am. Math. Soc. 355 4061-4091
  • [6] Zhang W(1990)Bilateral Bailey lemma and Rogers–Ramanujan identities Trans. Am. Math. Soc. 319 469-498
  • [7] Ismail MEH(2003)Tribasic integrals and identities of Rogers–Ramanujan type Proc. Lond. Math. Soc. 87 363-395
  • [8] Stanton D(undefined)Hall-Littlewood functions, plane partitions, and the Rogers–Ramanujan identities undefined undefined undefined-undefined
  • [9] Stembridge JR(undefined)Partial theta functions. I. Beyond the lost notebook undefined undefined undefined-undefined
  • [10] Warnaar SO(undefined)undefined undefined undefined undefined-undefined
1