Accession Number : AD0288010

Title :   HIGH-FREQUENCY APPROXIMATIONS TO ELLIPSOIDAL WAVE FUNCTIONS

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : ARSCOTT,F.M.

Report Date : JUL 1962

Pagination or Media Count : 1

Abstract : The ellipsoidal wave equation is the ordinary differential equation which arises when the reduced wave equation 2V+ 2V = 0 is separated in ellipsoidal coordinates; doubly-periodic solutions of this equation are known as ellipsoidal wave functions. Approximations to the latter, in the form of asymptotic series valid for 2 large positive or large negative, were given but the analysis was incomplete in that the values of two integral parameters were left undetermined. This gap is filled, the complete results re-calculated and the connections established between the asymptotic series and the standard solutions in various parts of the plane. As a by-product, some unpublished transformation formulae are given, linking ellipsoidal wave functions with negative 2 to those with positive 2. (Author)

Descriptors :   *DIFFERENTIAL EQUATIONS, *ELLIPSOIDS, FUNCTIONS(MATHEMATICS), QUANTUM THEORY

Distribution Statement : APPROVED FOR PUBLIC RELEASE