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Research Article | Open Access

New double-sum expansions for certain Mock theta functions

Qiuxia Hu1, Bilal Khan2, Serkan Araci3( ), Mehmet Acikgoz4
Department of Mathematics, Luoyang Normal University, Luoyang, 471934, China
School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China
Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University TR-27410 Gaziantep, Turkey
Department of Mathematics, Faculty of Science and Arts, Gaziantep University, TR-27310 Gaziantep, Turkey
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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.

Keywords

basic hypergeometric seriesMock theta functionsdouble sums
CLC number: Primary 05A30, 30C45; Secondary 11B65, 47B38

References

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 17225-17235
DOI: 10.3934/math.2022948

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Cite this article:
Hu Q, Khan B, Araci S, et al. New double-sum expansions for certain Mock theta functions. AIMS Mathematics, 2022, 7(9): 17225-17235. https://doi.org/10.3934/math.2022948

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Received: 06 June 2022
Revised: 18 July 2022
Accepted: 19 July 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)