The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of 2ψ2 series ∞ ∑n=−∞ (a, c;q)n (b,d;q)n z n . Three transformation formulae for this series due to Bailey are used to derive various transformation and summation formulae for both these mock theta functions and the corresponding bilateral series. New and existing summation formulae for these bilateral series are also used to make explicit in a number of cases the fact that for a mock theta function, say χ(q), and a root of unity in a certain class, say ζ , that there is a theta function θχ (q) such that lim q→ζ (χ(q)−θχ (q)) exists, as q → ζ from within the unit circle.
Springer Proceedings in Mathematics & Statistics
McLaughlin, J. (2017). Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series. Springer Proceedings in Mathematics & Statistics, 221, 503-531. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/68
Preprint version is available here.
From the conference proceedings of the 2016 Gainesville International Number Theory Conference in honour of Krishna Alladi