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

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

2006-06-30

arxiv.org/abs/math/0606781v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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 $\theta$-function.

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