Abstract
Recently, Hirschhorn investigated vanishing coefficients of the arithmetic progressions in the following two q-series expansions
He proved that for In this paper, we further study these two q-series expansions and obtain the generating functions of
and
by using two MAPLE packages, qseries and thetaids, due to Jie Frye and Frank Garvan. The signs of
and
are determined, which imply Hirschhorn’s results given above.