Methods and Applications of Analysis

Volume 23 (2016)

Number 2

Asymptotic analysis of difference equations with quadratic coefficients

Pages: 155 – 172



Xiang-Sheng Wang (Department of Mathematics, University of Louisiana, Lafayette, La., U.S.A.)


In this paper, we study asymptotic solutions of second-order difference equations with quadratic coefficients. According to the parameter values, we classify the difference equations into three cases and derive Plancherel–Rotach type asymptotic formulas of the solutions respectively. As direct applications of our main results, we also provide asymptotic formulas of associated Meixner–Pollaczek polynomials, associated Meixner polynomials, and associated Laguerre polynomials, respectively.


asymptotic analysis, difference equations, associated polynomials

2010 Mathematics Subject Classification

39A05, 41A60

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Published 30 June 2016