Asymptotics for q-expansions involving partial theta functions

作者：Kim Byungchan; Kim Eunmi^*; Seo Jeehyeon

来源：Discrete Mathematics, 2015, 338(2): 180-189.

DOI：10.1016/j.disc.2014.09.011

• Partial theta function
• Asymptotics
• Effective bound
• Partitions
• Crank
• Rank

We obtain effective asymptotics for the coefficients of q-expansions which involve partial theta functions. As applications, we obtain effective asymptotics for ranks, and cranks of integer partitions. Moreover, from these effective estimates, we obtain asymptotic inequalities among them with effective lower bounds.

• 出版日期2015-2-6