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.