On A Limiting Relation Between Ramanujan's Entire Function $A_{q}(z)$ And $θ$-Function

Details On A Limiting Relation Between Ramanujan's Entire Function $A_{q}(z)$ And $θ$-Function On A Limiting Relation Between Ramanujan's Entire Function $A_{q}(z)$ And $θ$-Function

2006-06-30

arxiv.org/abs/math/0606782v2

Mathematics

Classical Analysis and ODEs

15 pages

Scientific paper

We will use a discrete analogue of the classical Laplace method to show that
the main term of the asymptotic expansions of certain entire functions,
including Ramanujan's entire function $A_{q}(z)$, can be expressed in terms of
$\theta$-functions.

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