Asymptotic expansions of certain partial theta functions

Berndt, Bruce; Kim, Byungchan

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

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.

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