Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations

  title={Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations},
  author={T. Mark Dunster},
  journal={arXiv: Classical Analysis and ODEs},
  • T. M. Dunster
  • Published 12 October 2020
  • Mathematics
  • arXiv: Classical Analysis and ODEs
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions involve exponential, Airy and Scorer functions and slowly varying analytic coefficient functions involving simple coefficients. The approximations are uniformly valid for large values of the parameter and unbounded real and complex values of the argument… 
2 Citations
Nield-Kuznetsov Functions and Laplace Transforms of Parabolic Cylinder Functions
  • T. M. Dunster
  • Computer Science, Mathematics
    SIAM J. Math. Anal.
  • 2021
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  • T. M. Dunster
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2020
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