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arxiv: math/0703030 · v4 · submitted 2007-03-01 · 🧮 math.CA · math.CV

Scaled Asymptotics For Some q-Series

classification 🧮 math.CA math.CV
keywords functionasymptoticsgammapolynomialsalphaapproachingbesseleuler
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In this work we investigate the asymptotics for Euler's $q$-Exponential $E_{q}(z)$, $q$-Gamma function $\Gamma_{q}(z)$, Ramanujan's function $A_{q}(z)$, Jackson's $q$-Bessel function $J_{\nu}^{(2)}$(z;q) of second kind, Stieltjes-Wigert orthogonal polynomials $S_{n}(x;q)$ and $q$-Laguerre polynomials $L_{n}^{(\alpha)}(x;q)$ as $q$ approaching 1.

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