English

Scaled Asymptotics For Some $q$-Series As $q$ Approaching Unit

Classical Analysis and ODEs 2007-11-28 v1

Abstract

In this work we investigate Plancherel-Rotach type asymptotics for some qq-series as q1q\to1. These qq-series generalize Ramanujan function Aq(z)A_{q}(z); Jackson's qq-Bessel function Jν(2)J_{\nu}^{(2)}(z;q), Ismail-Masson orthogonal polynomials(q1q^{-1}-Hermite polynomials) hn(xq)h_{n}(x|q), Stieltjes-Wigert orthogonal polynomials Sn(x;q)S_{n}(x;q), qq-Laguerre orthogonal polynomials Ln(α)(x;q)L_{n}^{(\alpha)}(x;q) and confluent basic hypergeometric series.

Keywords

Cite

@article{arxiv.0711.4161,
  title  = {Scaled Asymptotics For Some $q$-Series As $q$ Approaching Unit},
  author = {Ruiming Zhang},
  journal= {arXiv preprint arXiv:0711.4161},
  year   = {2007}
}

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R2 v1 2026-06-21T09:47:33.228Z