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Mock theta函数的Hecke型双重和
杨继真¹, 宋捍飞², 张之正^1,3
1.洛阳师范学院数学科学学院, 洛阳河南 471934;2.上海师范大学数理学院, 上海 200234;3.河南师范大学数学与信息科学学院, 新乡河南 453001

摘要:

本文研究了mock theta函数对应的Hecke型双重和的问题.利用Bailey对的方法,获得了三个与七阶和十阶mock theta函数相关的等式和两个新的与三阶mock theta函数相关的Hecke型双重和.

关键词: mock theta函数 Hecke型双重和 Bailey对 q-级数

DOI：

分类号:O173

基金项目:Supported by National Natural Science Foundation of China (11871258); the Young Backbone Teachers in Henan Province (2020GGJS194); the Young Backbone Teachers in Luoyang Normal College (2019XJGGJS-10).

HECKE-TYPE DOUBLE SUMS AS MOCK THETA FUNCTIONS

YANG Ji-zhen¹, SONG Han-fei², ZHANG Zhi-zheng^1,3

1.Department of Mathematics, Luoyang Normal University, Luoyang 471934, China;2.Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;3.College of Mathematics and Information Science, Henan Normal University, Xinxiang 453001, China

Abstract:

The main purpose of this paper is to present Hecke-type double sums associated with mock theta functions. By using the method of Bailey pairs, we obtain three known identities for the seventh and tenth order mock theta functions and two new Hecke-type double sums as third order mock theta functions.

Key words: mock theta functions Hecke-type double sums Bailey pairs q-series