Published January 1960
| Published
Journal Article
Open
Asymptotic Solutions of Differential Equations with Transition Points or Singularities
- Creators
- Erdélyi, A.
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.
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.Attached Files
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Additional details
- Eprint ID
- 12105
- Resolver ID
- CaltechAUTHORS:ERDjmp60
- Office of Naval Research
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2008-10-23Created from EPrint's datestamp field
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2023-05-16Created from EPrint's last_modified field