Vanishing coefficients in some -series expansions
arXiv:1912.11185
Abstract
Motivated by the recent work of Hirschhorn on vanishing coefficients of the arithmetic progressions in certain -series expansions, we study some variants of these -series and prove some comparable results. For instance, let \begin{align*} (-q,-q^{4};q^{5})_{\infty}^{2}(q^{4},q^{6};q^{10})_{\infty}=\sum_{n=0}^{\infty}a_{1}(n)q^{n}, \end{align*} then \begin{align*} a_{1}(5n+3)=0. \end{align*}
11 pages