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Numerische Mathematik

, Volume 94, Issue 1, pp 147–194 | Cite as

Asymptotic expansions for second-order linear difference equations with a turning point

  • Z. Wang
  • R. Wong

Summary.

 A turning-point theory is developed for the second-order difference equation
$$$$
where the coefficients A n and B n have asymptotic expansions of the form
$$$$
θ≠0 being a real number. In particular, it is shown how the Airy functions arise in the uniform asymptotic expansions of the solutions to this three-term recurrence relation. As an illustration of the main result, a uniform asymptotic expansion is derived for the orthogonal polynomials associated with the Freud weight exp(−x 4 ), xℝ.

Keywords

Real Number Asymptotic Expansion Difference Equation Turning Point Orthogonal Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Z. Wang
    • 1
  • R. Wong
    • 1
  1. 1.Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong; e-mail: mawong@cityu.edu.ukGB

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