A difference equation approach to Plancherel-Rotach asymptotics forq-orthogonal polynomials

摘要

In this paper, we employ a difference equation approach to study the Plancherel-Rotach asymptotics ofq-orthogonal polynomials about their largest zeros. Our method forq-difference equations is an analogue to the turning point problem for Hermite differential equations. It works well in the toy problems of Stieltjes-Wigert polynomials andq-1-Hermite polynomials.