Scaled Asymptotics for Some q-Series as q Approaches One

Details Scaled Asymptotics for Some q-Series as q Approaches One Scaled Asymptotics for Some q-Series as q Approaches One

2009-12-15

arxiv.org/abs/0912.3030v3

Mathematics

General Mathematics

16pages

Scientific paper

In this work we investigate Plancherel-Rotach type asymptotics for some $q$-series as $q\to1$. These $q$-series generalize Ramanujan function $A_{q}(z)$ ($q$-Airy function), Jackson's $q$-Bessel function $J_{\nu}^{(2)}$(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 $L_{n}^{(\alpha)}(x;q)$ and confluent basic hypergeometric series.

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