Plancherel–Rotach asymptotics for certain basic hypergeometric series

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• 作者：Ruiming Zhang
• 关键词：q-series ; q-orthogonal polynomials ; Euler's q-exponential ; q-Airy function of K. Kajiwara ; T. Masuda ; M. Noumi ; Y. Ohta and Y. Yamada ; q-Airy function (Ramanujan function) ; Jackson's q-Bessel function ; Ismail
• 刊名：Advances in Mathematics
• 出版年：2008
• 出版时间：1 March 2008
• 年：2008
• 卷：217
• 期：4
• 页码：1588-1613
• 全文大小：212 K

文摘

In this work we study the chaotic and periodic asymptotics for the confluent basic hypergeometric series. For a fixed q(0,1), the asymptotics for Euler's q-exponential, q-Gamma function Γ_q(x), q-Airy function of K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta and Y. Yamada, Ramanujan function (q-Airy function), Jackson's q-Bessel function of second kind, Ismail–Masson orthogonal polynomials (q⁻¹-Hermite polynomials), Stieltjes–Wigert polynomials, q-Laguerre polynomials could be derived as special cases.