Two New Mock Theta Double Sums
Received:March 29, 2022  Revised:June 27, 2022
Key Words: mock theta double sums   Bailey pair   Appell-Lerch sums   theta series  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11871258; 12271234), the Young Backbone Teachers in Henan Province (Grant No.2020GGJS194), the First-Class Courses in Henan Province (Grant No.[2020]13099) and the Young Backbone Teachers in Luoyang Normal College (Grant No.2019XJGGJS10).
Author NameAffiliation
Jizhen YANG Department of Mathematics, Luoyang Normal University, Henan 471934, P. R. China 
Hanfei SONG Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China 
Zhizheng ZHANG Department of Mathematics, Luoyang Normal University, Henan 471934, P. R. China
College of Mathematics and Information Science, Henan Normal University, Henan 453001, P. R. China 
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      Recently, Zhang and Li presented five mock theta functions as $q$-hypergeometric double sums by using a Bailey pair. In this paper, employing the same Bailey pair, we further establish two new mock theta double sums in terms of Appell-Lerch sums and theta series. Indeed, identities between a new mock theta function and classical mock theta functions are obtained.
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