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On A Relation Between $q$-Exponential And $θ$-Function

Ruiming Zhang
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Abstract

We will use a discrete analogue of the classical Laplace method to show that for infinitely many positive integers $n$, the main term of the asymptotic expansion of the scaled $q$-exponential $(-q^{-nt+1/2}u;q)_{\infty}$ could be expressed in $θ$-function.

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Ruiming Zhang. 2006-06-30. On A Relation Between $q$-Exponential And $θ$-Function. https://arxiv.org/abs/math/0606781

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