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arXiv · 1206.4737

Plancherel_Rotach Asymptotics for q-Orthogonal Polynomials

Mourad E. H. Ismail·Xin Li
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Abstract

We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q^{-1}-Hermite polynomials of Askey, Ismail and Masson, q-Laguerre polynomials, and the Stieltjes-Wigert polynomials. We also introduce a one parameter family of solutions to the q-difference equation of the Ramanujan function.

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Mourad E. H. Ismail, Xin Li. 2012-06-20. Plancherel_Rotach Asymptotics for q-Orthogonal Polynomials. https://arxiv.org/abs/1206.4737

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