Asymptotic transformations of q-series

For the q-series Sigma(n=0)(infinity)a(n)q(bn2+cn)/(q)(n) we construct a companion q-series such that the asymptotic expansions of their logarithms as q --> 1(-) differ only in the dominant few terms. The asymptotic expansion of their quotient then has a simple closed form; this gives rise to a new q-hypergeometric identity. We give an asymptotic expansion of a general class of q-series containing some of Ramanujan's mock theta functions and Selberg's identities.