Certain bilateral basic hypergeometric transformations and mock theta functions (Q1293781)

Ramanujan's ten mock theta functions of order five are made bilatral by extending the range of summation. Using appropriate \({_2\psi_2}\) transformations, the author derives alternative expressions for these bilateral mock theta functions. An example is, \[ F_{0c}(q)= \sum^\infty_{-\infty} {q^{2n^2}\over (q; q^2)_n}= \sum^\infty_{-\infty} (-1)^n q^{n^2}(q; q^2)_n.\tag{\(*\)} \] A number of relations between the functions are established; some of them involve also certain other series, whose summands are akin to those shown in \((*)\).