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Asymptotic Solutions of Differential Equations with Transition Points or Singularities

Erdélyi, A. (1960) Asymptotic Solutions of Differential Equations with Transition Points or Singularities. Journal of Mathematical Physics, 1 (1). pp. 16-26. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:ERDjmp60

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Abstract

Asymptotic solutions of d^2y/dx^2+[^2p(x)+r(x,λ)]y=0 are found when lambda is a large parameter and r is "small" in comparison with λ^2p, except at a single point where either p has a simple zero, or p a pole of the first order and r a pole of the second order. The results are applied to Bessel functions, and to Hermite and Laguerre polynomials. The resulting asymptotic forms are valid uniformly in x.


Item Type:Article
Related URLs:
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http://dx.doi.org/10.1063/1.1703631DOIUNSPECIFIED
http://link.aip.org/link/?JMAPAQ/1/16/1PublisherUNSPECIFIED
Additional Information:© 1960 The American Institute of Physics. Received December 7, 1959. This paper is based on several reports by the author and others. These reports were prepared under contract with the Office of Naval Research and are listed with all other references in the Bibliography at the end of this paper under 1, 3, 4, 5, 8, 9, 19, 20. References appear in the text in brackets.
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Office of Naval ResearchUNSPECIFIED
Record Number:CaltechAUTHORS:ERDjmp60
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:ERDjmp60
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Deposited On:23 Oct 2008 16:26
Last Modified:26 Dec 2012 10:27

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