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

Ruiming Zhang

arxiv: math/0606782 · v2 · submitted 2006-06-30 · 🧮 math.CA · math.CV

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

Ruiming Zhang This is my paper

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keywords entirefunctionfunctionsramanujanthetaanalogueasymptoticcertain

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

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