一类新的m重Rogers-Ramanujan恒等式及应用

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 851-864.

一类新的m重Rogers-Ramanujan恒等式及应用

张之正^1,^2,*(),李晓倩²()

¹ 洛阳师范学院数学科学学院河南洛阳 471934
² 河南师范大学数学与信息科学学院河南新乡 453001

收稿日期:2017-05-16 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 张之正 E-mail:zhzhzhang-yang@163.com;791408196@qq.com
作者简介:李晓倩, E-mail:791408196@qq.com
基金资助:
国家自然科学基金(11871258)

A Class of New m-Multisum Rogers-Ramanujan Identities and Applications

Zhizheng Zhang^1,^2,*(),Xiaoqian Li²()

¹ Department of Mathmetics, Luoyang Normal University, Henan Luoyang 471934
² College of Mathematics and Information Science, Henan Normal University, Henan Xinxiang 453001

Received:2017-05-16 Online:2019-08-26 Published:2019-09-11
Contact: Zhizheng Zhang E-mail:zhzhzhang-yang@163.com;791408196@qq.com
Supported by:
the NSFC(11871258)

摘要/Abstract

摘要：

Rogers-Ramanujan恒等式是分拆理论和组合学中著名的恒等式，被广泛的证明和推广.该文应用双边Bailey引理和迭代技巧建立一类新的多重和Rogers-Ramanujan恒等式.

关键词: 双边Bailey引理, 移位Bailey对, 多重Rogers-Ramanujan恒等式

Abstract:

Rogers-Ramanujan identities are among the most famous q-series in partition theory and combinatorics, they have been proved and generalized widely. The purpose of this paper is to establish a class of new multisum Rogers-Ramanujan identities by applying the bilateral Bailey lemma and iterating technique.

Key words: Bilateral Bailey lemma, Shifted Bailey pair, Multisum Rogers-Ramanujan identities

中图分类号:

O157.1

张之正,李晓倩. 一类新的m重Rogers-Ramanujan恒等式及应用[J]. 数学物理学报, 2019, 39(4): 851-864.

Zhizheng Zhang,Xiaoqian Li. A Class of New m-Multisum Rogers-Ramanujan Identities and Applications[J]. Acta mathematica scientia,Series A, 2019, 39(4): 851-864.

参考文献 16

1	Agarwal A , Andrew G E , Bressoud D . The Bailey lattice. J Indian Math Soc, 1987, 51: 57- 73
2	Andrews G E . An analytic generalization of the Rogers-Ramanujan identities for odd moduli. Proc National Academy of Science, USA, 1974, 71 (10): 4082- 4085 doi: 10.1073/pnas.71.10.4082
3	Andrews G E . Multiple series Rogers-Ramanujan type identities. Pac J Math, 1984, 114: 267- 283 doi: 10.2140/pjm.1984.114.267
4	Andrews G E. q-Series:Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra. Providence, RI:Amer Math Soc, 1986
5	Andrews G E , Schilling A , Warnaar S O . An A₂ Bailey lemma and Rogers-Ramanujan-type identities. J Amer Math Soc, 1999, 12 (3): 677- 702 doi: 10.1090/S0894-0347-99-00297-0
6	Bailey W N . Identities of the Rogers-Ramanujan type. Proc London Math Soc, 2002, 66: 529- 549 doi: 10.1112/S0024610702003617
7	Bressoud D , Ismail M , Stanton D . Change of base in Bailey pairs. Ramanujan J, 2000, 4: 435- 453 doi: 10.1023/A:1009824218230
8	Berkovich A , McCoy B M , Schilling A . N=2 supersymmetry and Bailey pairs. Physical A, 1996, 228: 33- 62
9	Frederic J . Shifted versions of the Bailey and WP-Poised Bailey lemmas. Ramnujan J, 2010, 23: 315- 333 doi: 10.1007/s11139-010-9282-x
10	Gasper G , Rahman M . Basic Hypergeometric Series. Cambridge: Cambridge University Press, 1990
11	Andrew V Sills . On identities of the Rogers-Ramanujan type. Ramanujan J, 2006, 11: 403- 429 doi: 10.1007/s11139-006-8483-9
12	Slater L J . A new proof of Rogers's transformations of infinite series. Proc London Math Soc, 1951, 53 (2): 460- 475
13	Slater L J . Further identities of the Rogers-Ramanujan type. Proc London Math Soc, 1952, 54: 147- 167
14	Watson G N . A new proof of the Rogers-Ramanujan identities. J London Math Soc, 1929, 4: 4- 9
15	Chu W , Yan Q . Jacobi's triple product identity and theta functions. Math Commun, 2011, 16: 191- 203
16	朱军明, 张之正. 几个级数-乘积型恒等式与Dedekind Eta函数展开式. 数学物理学报, 2015, 35A (1): 110- 117
	Zhu J M , Zhang Z Z . Some series-product identities and expansions on Dedekind's Eta function. Acta Math Sci, 2015, 35A (1): 110- 117