Some results on vanishing coefficients in infinite product expansions

Nayandeep Deka Baruah, Mandeep Kaur

Recently, M. D. Hirschhorn proved that, if ${\sum }_{n=0}^{\infty }{a}_n{q}^n:=(-q,-q^4;q^5{)}_{\infty }(q,q^9;q^{10}{)}_{\infty }^3$ and $\sum_{n=0}^\infty b_nq^n:=(-q^2,-q^3;q^5)_\infty(q^3,q^7;q…