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arXiv · 0711.4161

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

Ruiming Zhang
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Abstract

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

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Ruiming Zhang. 2007-11-27. Scaled Asymptotics For Some $q$-Series As $q$ Approaching Unit. https://arxiv.org/abs/0711.4161

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