  We define two finite q-analogs of certain multiple harmonic series with an
arbitrary number of free parameters, and prove identities for these q-analogs,
expressing them in terms of multiply nested sums involving the Gaussian
binomial coefficients. Special cases of these identities--for example, with all
parameters equal to 1--have occurred in the literature. The special case with
only one parameter reduces to an identity for the divisor generating function,
which has received some attention in connection with problems in sorting
theory. The general case can be viewed as a duality result, reminiscent of the
duality relation for the ordinary multiple zeta function.
