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New mock theta functions and formulas for basic hypergeometric series

Part of: Combinatorics Sequences and sets Basic hypergeometric functions Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  22 August 2023

Olivia X. M. Yao
Olivia X. M. Yao*
Affiliation:
School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou, Jiangsu Province, P. R. China ([email protected])
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Abstract

In recent years, mock theta functions in the modern sense have received great attention to seek examples of q-hypergeometric series and find their alternative representations. In this paper, we discover some new mock theta functions and express them in terms of Hecke-type double sums based on some basic hypergeometric series identities given by Z.G. Liu.

Keywords

mock theta functionsHecke-type double sumsbasic hypergeometric series

MSC classification

Primary: 33D15: Basic hypergeometric functions in one variable, $_rphi_s$ 05A30: $q$-calculus and related topics 11B65: Binomial coefficients; factorials; $q$-identities 11F11: Holomorphic modular forms of integral weight
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 3 , August 2023 , pp. 868 - 896
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Copyright
© The Author(s), 2023. Published by Cambridge University Press.

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