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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. doi:10.1063/1.1703631.

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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.

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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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Deposited On:23 Oct 2008 16:26
Last Modified:08 Nov 2021 22:25

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