On partial sums of mock theta functions of order three (Q1370309)

Ramanujan's mock theta functions of order three can be represented as limiting cases of the basic hypergeometric series \({_2\Phi_1}(\alpha,q;\beta;q;x)\). By means of Heine's transformation \[ (x,c)_\infty {_2\Phi_1}(a,b;c;q;x)=(b,ax)_\infty{_2\Phi_1}\big( {\textstyle{c\over b}}, x;ax;q;b\bigr) \] this representation is transformed to similar series representations. The author defines partial mock theta functions of order three as partial sums of these series. He then derives some identities and continued fraction expansions for these functions.