Properties of some new bilateral mock theta functions. (English) Zbl 1438.33025
Summary: Bilateral mock theta functions were obtained and studied in [M. Ahmad et al., Electron. J. Math. Analysis Appl. 7, No. 2, 216–229 (2019; Zbl 1409.33012)]. We express them in terms of Lerch’s transcendental function \(f(x, \xi; q, p)\). We also express some bilateral mock theta functions as sum of other mock theta functions. We generalize these functions and show that these generalizations are \(F_q\) functions. We give an integral representation for these generalized functions.
MSC:
| 33D15 | Basic hypergeometric functions in one variable, \({}_r\phi_s\) |
| 11B65 | Binomial coefficients; factorials; \(q\)-identities |
Citations:
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