Asymptotic expansions of certain partial theta functions

Bruce C. Berndt; Byungchan Kim

doi:10.1090/S0002-9939-2011-11062-1

Asymptotic expansions of certain partial theta functions

Bruce C. Berndt, Byungchan Kim

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	3779-3788
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-2011-11062-1
State	Published - Nov 2011

Keywords

Asymptotic expansion
Dirichlet series associated with a polynomial
Euler numbers
False theta functions
Hermite polynomials
Partial theta functions
Ramanujan's notebooks
Theta functions

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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keywords = "Asymptotic expansion, Dirichlet series associated with a polynomial, Euler numbers, False theta functions, Hermite polynomials, Partial theta functions, Ramanujan's notebooks, Theta functions",

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KW - False theta functions

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