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Zbl 1064.39018
Geronimo, Jeffrey S.; Bruno, Oscar; van Assche, Walter
WKB and turning point theory for second-order difference equations. (English)
[A] Janas, Jan (ed.) et al., Spectral methods for operators of mathematical physics. Proceedings of the international conference on operator theory and its applications in mathematical physics, OTAMP, Bedlewo, Poland, 2002. Basel: Birkhäuser. Operator Theory: Advances and Applications 154, 101-138 (2004). ISBN 3-7643-7133-1/hbk

Summary: A turning point method for difference equations is developed. This method is coupled with the LG-WKB method via matching to provide approximate solutions to the initial value problem. The techniques developed are used to provide strong asymptotics for Hermite polynomials.

MSC 2000:: *39A12 Discrete version of topics in analysis
39A11 Stability of difference equations
34M60 Singular perturbation problems in the complex domain

Keywords: difference equations; orthogonal polynomials; turning point method; LG-WKB method; initial value problem; strong asymptotics; Hermite polynomials

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