
Accession Number : AD0288010
Title : HIGHFREQUENCY 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; doublyperiodic 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 recalculated and the connections established between the asymptotic series and the standard solutions in various parts of the plane. As a byproduct, some unpublished transformation formulae are given, linking ellipsoidal wave functions with negative 2 to those with positive 2.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