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WKB and turning point theory for second-order difference equations. (English) Zbl 1064.39018
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 (ISBN 3-7643-7133-1/hbk). Operator Theory: Advances and Applications 154, 101-138 (2004).
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. For the entire collection see [Zbl 1051.47002].

39A12Discrete version of topics in analysis
39A11Stability of difference equations (MSC2000)
34M60Singular perturbation problems in the complex domain