On the positive coefficients of two families of $q$-series

Ji-Cai Liu, Kong-Lian Liao

Let $S$ be a finite set of pairwise coprime positive integers and $A{x}^2+Bx$ be an integer valued polynomial with $A>B\ge 0$. For integers $k\ge 1$ and $n\ge 0$, the coefficients $…