  Recently, M. D. Hirschhorn proved that, if $\sum_{n=0}^\infty a_nq^n :=
(-q,-q^4;q^5)_\infty(q,q^9;q^{10})_\infty^3$ and $\sum_{n=0}^\infty
b_nq^n:=(-q^2,-q^3;q^5)_\infty(q^3,q^7;q^{10})_\infty^3$, then
$a_{5n+2}=a_{5n+4}=0$ and $b_{5n+1}=b_{5n+4}=0$. Motivated by the work of
Hirschhorn, D. Tang proved some comparable results including the following: If
$ \sum_{n=0}^\infty c_nq^n := (-q,-q^4;q^5)_\infty^3(q^3,q^7;q^{10})_\infty$
and $\sum_{n=0}^\infty d_nq^n :=
(-q^2,-q^3;q^5)_\infty^3(q,q^9;q^{10})_\infty$, then $c_{5n+3}=c_{5n+4}=0$ and
$d_{5n+3}=d_{5n+4}=0$.
  In this paper, we prove that $a_{5n}=b_{5n+2}$, $a_{5n+1}=b_{5n+3}$,
$a_{5n+2}=b_{5n+4}$, $a_{5n-1}=b_{5n+1}$, $c_{5n+3}=d_{5n+3}$,
$c_{5n+4}=d_{5n+4}$, $c_{5n}=d_{5n}$, $c_{5n+2}=d_{5n+2}$, and
$c_{5n+1}>d_{5n+1}$. We also record some other comparable results not listed by
Tang.
