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Asymptotics for q-expansions involving partial theta functions
- Authors
- Kim, Byungchan; Kim, Eunmi; Seo, Jeehyeon
- Issue Date
- Feb-2015
- Publisher
- ELSEVIER
- Keywords
- Partial theta function; Asymptotics; Effective bound; Partitions; Crank; Rank
- Citation
- DISCRETE MATHEMATICS, v.338, no.2, pp 180 - 189
- Pages
- 10
- Journal Title
- DISCRETE MATHEMATICS
- Volume
- 338
- Number
- 2
- Start Page
- 180
- End Page
- 189
- ISSN
- 0012-365X
1872-681X
- 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. (C) 2014 Elsevier B.V. All rights reserved.
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