Asymptotic Solutions of Differential Equations with Transition Points or Singularities
- 1 January 1960
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 1 (1) , 16-26
- https://doi.org/10.1063/1.1703631
Abstract
Asymptotic solutions of d 2 y/dx 2 +[λ 2 p(x)+r(x,λ)]y=0 are found when λ is a large parameter and r is ``small'' in comparison with λ2 p, 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.Keywords
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