Some identities of certain basic hypergeometric series and their applications to mock theta functions

In this paper, we first obtain the corresponding transformation formulas of the basic bilateral hypergeometric series involving universal mock theta functions. Meanwhile, some identities of bilateral series associated with classical mock theta functions are deduced. From the duals of second type for...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics Vol. 54; no. 4; pp. 1214 - 1225
Main Authors: Zhang, Zhizheng, Song, Hanfei
Format: Journal Article
Language:English
Published: New Delhi Indian National Science Academy 01.12.2023
Springer Nature B.V
Subjects:
Applications of Mathematics
Equality
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Research
11F27
Bilateral series
Hecke-type identities
11B65
Basic hypergeometric series
Mock theta functions
33D15
ISSN:0019-5588, 0975-7465
Online Access:Get full text
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Summary:In this paper, we first obtain the corresponding transformation formulas of the basic bilateral hypergeometric series involving universal mock theta functions. Meanwhile, some identities of bilateral series associated with classical mock theta functions are deduced. From the duals of second type for universal mock theta functions, two new Hecke-type identities are derived. Some special cases for classical mock theta functions are also obtained immediately. Finally, an identity for K 2 ( x , q ) is discussed by a transformation formula.
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ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-022-00335-5