Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series
arXiv:1906.11997 · doi:10.1007/978-3-319-68376-8_29
Abstract
The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of series \[ \sum_{n=-\infty}^{\infty}\frac{(a,c;q)_n}{(b,d;q)_n}z^n. \] 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 , and a root of unity in a certain class, say , that there is a theta function such that \[ \lim_{q \to ζ}(χ(q) - θ_χ(q)) \] exists, as from within the unit circle.
27 pages