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Scaled Asymptotics For Some $q$-Series

Ruiming Zhang
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Abstract

In this work we investigate the asymptotics for Euler's $q$-Exponential $E_{q}(z)$, $q$-Gamma function $Γ_{q}(z)$, Ramanujan's function $A_{q}(z)$, Jackson's $q$-Bessel function $J_ν^{(2)}$(z;q) of second kind, Stieltjes-Wigert orthogonal polynomials $S_{n}(x;q)$ and $q$-Laguerre polynomials $L_{n}^{(α)}(x;q)$ as $q$ approaching 1.

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Ruiming Zhang. 2007-05-05. Scaled Asymptotics For Some $q$-Series. https://arxiv.org/abs/math/0703030

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