| 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
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| 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 Name | Affiliation | | 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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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2023.02.010 |
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