Ramanujan-type partial theta identities and conjugate Bailey pairs

被引:31
作者
Lovejoy, Jeremy [1 ]
机构
[1] Univ Paris 07, CNRS, LIAFA, F-75205 Paris 13, France
关键词
Bailey pairs; Conjugate Bailey pairs; Partial theta identities; Mixed mock modular forms; LOST NOTEBOOK;
D O I
10.1007/s11139-011-9356-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Residual identities of Ramanujan-type partial theta identities are tailor-made for producing conjugate Bailey pairs. This is carried out for partial theta identities in Ramanujan's lost notebook, a number of the partial theta identities of Warnaar, and for some new ones as well.
引用
收藏
页码:51 / 67
页数:17
相关论文
共 24 条
[1]  
Andrews G. E., 1986, CBMS REGIONAL C SERI, V66, pxii+130
[2]   RAMANUJAN LOST NOTEBOOK .7. THE 6TH ORDER MOCK THETA FUNCTIONS [J].
ANDREWS, GE ;
HICKERSON, D .
ADVANCES IN MATHEMATICS, 1991, 89 (01) :60-105
[3]   RAMANUJANS LOST NOTEBOOK .1. PARTIAL THETA-FUNCTIONS [J].
ANDREWS, GE .
ADVANCES IN MATHEMATICS, 1981, 41 (02) :137-172
[4]   BAILEY CHAINS AND GENERALIZED LAMBERT SERIES .1. 4 IDENTITIES OF RAMANUJAN [J].
ANDREWS, GE .
ILLINOIS JOURNAL OF MATHEMATICS, 1992, 36 (02) :251-274
[5]   THE 5TH AND 7TH ORDER MOCK THETA-FUNCTIONS [J].
ANDREWS, GE .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 293 (01) :113-134
[6]   PARTITIONS AND INDEFINITE QUADRATIC-FORMS [J].
ANDREWS, GE ;
DYSON, FJ ;
HICKERSON, D .
INVENTIONES MATHEMATICAE, 1988, 91 (03) :391-407
[7]   The Bailey transform and false theta functions [J].
Andrews, George E. ;
Warnaar, S. Ole .
RAMANUJAN JOURNAL, 2007, 14 (01) :173-188
[8]  
Bailey W.N., 1948, Proc. Lond. Math. Soc., V50, P1, DOI DOI 10.1112/PLMS/S2-50.1.1
[9]   SOME IDENTITIES FOR TERMINATING Q-SERIES [J].
BRESSOUD, DM .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1981, 89 (MAR) :211-223
[10]  
Fine NJ, 1988, BASIC HYPERGEOMETRIC SERIES AND APPLICATIONS