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Asymptotic Approximations for Prolate Spheroidal Wave Functions
Author(s) -
Miles John W.
Publication year - 1975
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1975544315
Subject(s) - bessel function , prolate spheroid , wave function , approximations of π , computation , mathematics , mathematical analysis , coulomb wave function , prolate spheroidal coordinates , function (biology) , coulomb , physics , quantum mechanics , algorithm , evolutionary biology , biology , electron
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 ↑∞.