English

On A Relation Between $q$-Exponential And $\theta$-Function

Classical Analysis and ODEs 2007-05-23 v1 Complex Variables

Abstract

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

Keywords

Cite

@article{arxiv.math/0606781,
  title  = {On A Relation Between $q$-Exponential And $\theta$-Function},
  author = {Ruiming Zhang},
  journal= {arXiv preprint arXiv:math/0606781},
  year   = {2007}
}