| Abstract: |
| We develop an intuitive approach to the
Plancherel-Rotach asymptotics around the largest zero of a
polynomial satisfying a linear functional equation. We first
treat the toy problem of Hermite polynomials in order to explain the
process by which we determine the correct Plancherel-Rotach
asymptotics. Then we treat the Stieltjes-Wigert polynomials and some other $q$-orthogonal polynomials. Our approach does not use any refined properties of these orthogonal polynomials. We only use the second order operator whether it is differential, difference or $q$-difference.
This is joint work with Mourad Ismail. |
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