4 papers
A combinatorial proof for the positivity of the normalized Jacobi triple product tails
Xiangyu Ding, Lisa Hui Sun
For , 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}…
Proof of Merca's stronger conjecture on truncated Jacobi triple product series
Xiangyu Ding, Lisa Hui Sun
In the study of theta series and partition functions, Andrews and Merca, Guo and Zeng independently conjectured that a truncated Jacobi triple product series has nonnegative coeffi…
Truncated theta series from the Bailey lattice
Xiangyu Ding, Lisa Hui Sun
In 2012, Andrews and Merca obtained a truncated version of Euler's pentagonal number theorem and showed the nonnegativity related to partition functions. Meanwhile, Andrews-Merca a…
Bilateral Bailey pairs and Rogers-Ramanujan type identities
Xiangxin Liu, Lisa Hui Sun
Rogers-Ramanujan type identities occur in various branches of mathematics and physics. As a classic and powerful tool to deal with Rogers-Ramanujan type identities, the theory of B…