New double-sum expansions for certain Mock theta functions

Qiuxia Hu; Bilal Khan; Serkan Araci; Mehmet Acikgoz; Qiuxia Hu; Bilal Khan; Serkan Araci; Mehmet Acikgoz

doi:10.3934/math.2022948

AIMS Mathematics

2022, Volume 7, Issue 9: 17225-17235. doi: 10.3934/math.2022948

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Research article

New double-sum expansions for certain Mock theta functions

1.
Department of Mathematics, Luoyang Normal University, Luoyang, 471934, China
2.
School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China
3.
Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University TR-27410 Gaziantep, Turkey
4.
Department of Mathematics, Faculty of Science and Arts, Gaziantep University, TR-27310 Gaziantep, Turkey

Received: 06 June 2022 Revised: 18 July 2022 Accepted: 19 July 2022 Published: 22 July 2022
MSC : Primary 05A30, 30C45; Secondary 11B65, 47B38

The study of expansions of certain mock theta functions in special functions theory has a long and quite significant history. Motivated by recent correlations between $ q $-series and mock theta functions, we establish a new $ q $-series transformation formula and derive the double-sum expansions for mock theta functions. As an application, we state new double-sum representations for certain mock theta functions.
- basic hypergeometric series,
- Mock theta functions,
- double sums
Citation: Qiuxia Hu, Bilal Khan, Serkan Araci, Mehmet Acikgoz. New double-sum expansions for certain Mock theta functions[J]. AIMS Mathematics, 2022, 7(9): 17225-17235. doi: 10.3934/math.2022948

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Abstract

The study of expansions of certain mock theta functions in special functions theory has a long and quite significant history. Motivated by recent correlations between $ q $-series and mock theta functions, we establish a new $ q $-series transformation formula and derive the double-sum expansions for mock theta functions. As an application, we state new double-sum representations for certain mock theta functions.

References

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