Abstract:We establish an asymptotic expansion for a class of partial theta functions generalizing a result found in Ramanujan’s second notebook. Properties of the coefficients in this more general asymptotic expansion are studied, with connections made to combinatorics and a certain Dirichlet series.
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- Bruce C. Berndt
- Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
- MR Author ID: 35610
- Email: email@example.com
- Byungchan Kim
- Affiliation: School of Liberal Arts, Seoul National University of Science and Technology, 172 Gongreung 2 dong, Nowongu, Seoul, 139-743, Republic of Korea
- MR Author ID: 847992
- Email: firstname.lastname@example.org
- Received by editor(s): August 5, 2010
- Published electronically: July 7, 2011
- Additional Notes: The first author’s research was partially supported by grant No. H98230-07-1-0088 from the National Security Agency.
Part of this work was done while the second author was at the Korea Institute of Advanced Study
- Communicated by: Jim Haglund
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 139 (2011), 3779-3788
- MSC (2010): Primary 11F27, 33D15; Secondary 11B68
- DOI: https://doi.org/10.1090/S0002-9939-2011-11062-1
- MathSciNet review: 2823024