A Study of Bilateral New Mock Theta Functions

We define bilateral series for two sets of new mock theta functions-- one given by Andrews and the other by Bringmann et al. Not only the bilateral form of the mock theta functions in the two sets are equivalent they further come out to be equivalent to the bilateral form of the eighth order mock theta functions of Gordon and McIntosh. These bilateral series are expressed as a q-hypergeometric series and then represented by continued fractions. We extend the definition of the bilateral mock theta functions and show they are -functions and relations are then defined.