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Asymptotic Approximations for Prolate Spheroidal Wave Functions

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Uniformly valid (with respect to the independent variable) asymptotic approximations to the radial, prolate spheroidal wave functions are constructed from Bessel‐function and Coulomb‐wave‐function models for large values of the wave number c. The prolate angular functions also are considered, but more briefly. The emphasis is on qualitative accuracy (such as might be useful to the physicist), rather than on efficient algorithms for very accurate numerical computation, and the error factor for most of the approximations is 1 + O (1/c) as c↑∞.
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Document Type: Research Article

Affiliations: University of California, San Diego

Publication date: December 1, 1975

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