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An Asymptotic Study of a Glass of Ordinary Linear Differential Equations of the Second Order


Owens, Robert Hunter (1952) An Asymptotic Study of a Glass of Ordinary Linear Differential Equations of the Second Order. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/81ED-D440.


The asymptotic behavior, with respect to the large parameter µ, of two solutions of d2y/dx2 + µ2 [c2 - x2 + f(x, µ-1)] y = 0 is given where f(x, µ-1) = 0(µ-1) is subjected to suitable hypotheses and all variables are real. These solutions are approximated to by the parabolic cylinder functions Dv(±√2µ t) with v = µ a2/2 - 1/2 and t = Ø(x,µ-1). The function Ø(x,µ-1) and the quantity a2 are constructed as a part of the analysis in which the parameter µ is restricted in such a way that v is bounded away from the positive integers. The relative error of the approximating functions is uniform for all x.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics and Physics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Erdélyi, Arthur
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1952
Record Number:CaltechTHESIS:02082018-101404674
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10684
Deposited By: Benjamin Perez
Deposited On:08 Feb 2018 18:42
Last Modified:16 May 2023 21:17

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