New Fifth and Seventh Order Mock Theta Function Identities

被引：0
作者：
Frank G. Garvan
机构：
[1] University of Florida,Department of Mathematics
来源：
Annals of Combinatorics | 2019年 / 23卷
关键词：
Mock theta functions; Hecke–Rogers double sums; Bailey pairs; Conjugate Bailey pairs; Primary 33D15; Secondary 11B65; 11F27;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We give simple proofs of Hecke–Rogers indefinite binary theta series identities for the two Ramanujan’s fifth order mock theta functions χ0(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi _0(q)$$\end{document} and χ1(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi _1(q)$$\end{document} 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：18
相关论文
共 11 条
[1]  
Andrews GE(1986)The fifth and seventh order mock theta functions Trans. Amer. Math. Soc. 293 113-134
[2]  
Andrews GE(1989)Ramanujan’s “lost” notebook. VI. The mock theta conjectures. VI. Adv. Math. 73 242-255
[3]  
Garvan FG(1948)Identities of the Rogers-Ramanujan type Proc. London Math. Soc. 2 1-10
[4]  
Bailey WN(1988)On the seventh order mock theta functions Invent. Math. 94 661-677
[5]  
Hickerson D(2012)Ramanujan-type partial theta identities and conjugate Bailey pairs Ramanujan J. 29 51-67
[6]  
Lovejoy J(1951)A new proof of Rogers’s transformations of infinite series Proc. London Math. Soc. 2 460-475
[7]  
Slater LJ(2003)Partial theta functions. I. Beyond the lost notebook Proc. London Math. Soc. (3) 87 363-395
[8]  
Warnaar SO(1936)The mock theta functions (2) Proc. London Math. Soc. (2) 42 274-304
[9]  
Watson GN(2009)Ramanujan’s mock theta functions and their applications (after Zwegers and Ono-Bringmann) Astérisque 326 143-164
[10]  
Zagier D(2009)On two fifth order mock theta functions Ramanujan J. 20 207-214
12