A combinatorial proof for the positivity of the normalized Jacobi triple product tails

Xiangyu Ding, Lisa Hui Sun

For $k\ge 1$, we prove that \[ [q^n z^s]J_k(z,q)\geq 0, \qquad (n\geq 0,\ s\in\mathbb Z) \] for the normalized Jacobi triple product tails \[ J_k(z,q) = \frac{ \sum_{j=k}^{\infty}…