A difference equation approach to Plancherel-Rotach asymptotics for -orthogonal polynomials |
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| Authors: | Mourad Ismail Chun-Kong Law |
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| Institution: | 1. Department of Mathematics, University of Central Florida, Orlando, Florida;2. Department of Applied Mathematics, National Sun Yat-sen University, R.O.C., Kaohsiung, Taiwan |
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| Abstract: | In this paper, we employ a difference equation approach to study the Plancherel-Rotach asymptotics of  -orthogonal polynomials about their largest zeros. Our method for  -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 and  -Hermite polynomials. |
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| Keywords: | -Airy function -difference equations -Hermite polynomials Stieltjes-Wigert polynomials turning point problem |
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