DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click HERE
to register or log in.
HIGH-FREQUENCY APPROXIMATIONS TO ELLIPSOIDAL WAVE FUNCTIONS
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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 As a by-product, some unpublished transformation formulae are given, linking ellipsoidal wave functions with negative 2 to those with positive 2.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