New Fifth and Seventh Order Mock Theta Function Identities

被引：5
作者：
Garvan, Frank G. [1 ]
机构：
[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA
来源：
ANNALS OF COMBINATORICS | 2019年 / 23卷 / 3-4期
关键词：
Mock theta functions; Hecke-Rogers double sums; Bailey pairs; Conjugate Bailey pairs;
D O I：
10.1007/s00026-019-00438-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan's fifth order mock theta functions chi(0)(q) and chi(1)(q) and all three of Ramanujan's seventh order mock theta functions. We find that the coefficients of the three mock theta functions of order 7 are surprisingly related.
引用
收藏
页码：765 / 783
页数：19
相关论文
共 14 条
[1]  
Andrews G. E., 1998, CAMBRIDGE MATH LIB
[2]   RAMANUJAN LOST NOTEBOOK .4. THE MOCK-THETA-CONJECTURES [J].
ANDREWS, GE ;
GARVAN, FG .
ADVANCES IN MATHEMATICS, 1989, 73 (02) :242-255
[3]   THE 5TH AND 7TH ORDER MOCK THETA-FUNCTIONS [J].
ANDREWS, GE .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 293 (01) :113-134
[4]  
Bailey W.N., 1948, P LOND MATH SOC, V50, P1, DOI DOI 10.1112/PLMS/S2-50.1.1
[5]  
Gasper G., 2004, ENCY MATH ITS APPL, Vsecond
[6]   ON THE 7TH ORDER MOCK THETA-FUNCTIONS [J].
HICKERSON, D .
INVENTIONES MATHEMATICAE, 1988, 94 (03) :661-677
[7]   Ramanujan-type partial theta identities and conjugate Bailey pairs [J].
Lovejoy, Jeremy .
RAMANUJAN JOURNAL, 2012, 29 (1-3) :51-67
[8]  
Slater L.J., 1951, Proc. Lond. Math. Soc., V53, P460
[9]  
Subbarao M.V., 1971, P WASHINGTON STATE U, P80
[10]   Partial theta functions. I. Beyond the lost notebook [J].
Warnaar, SO .
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2003, 87 :363-395
12