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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotic expansions of certain partial theta functions
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by Bruce C. Berndt and Byungchan Kim PDF
Proc. Amer. Math. Soc. 139 (2011), 3779-3788 Request permission

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.
References
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Additional Information
  • Bruce C. Berndt
  • Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
  • MR Author ID: 35610
  • Email: berndt@illinois.edu
  • 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: bkim4@seoultech.ac.kr
  • 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