Elsevier

Discrete Mathematics

Volume 338, Issue 2, 6 February 2015, Pages 180-189
Discrete Mathematics

Asymptotics for q-expansions involving partial theta functions

Dedicated with admiration to Bruce Berndt on the occasion of his 75th birthday
https://doi.org/10.1016/j.disc.2014.09.011Get rights and content
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Abstract

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.

Keywords

Partial theta function
Asymptotics
Effective bound
Partitions
Crank
Rank

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