Accession Number : AD0715775

Title :   A Fortran Computer Program for Calculating the Prolate and Oblate Angle Functions of the First Kind and Their First and Second Derivates,

Corporate Author : NAVAL RESEARCH LAB WASHINGTON D C

Personal Author(s) : King,B. J. ; Van Buren,A. L.

Report Date : 30 NOV 1970

Pagination or Media Count : 25

Abstract : The Helmholtz or scalar wave equation (deli squared + k squared) PSI = 0 is separable in both prolate and oblate spheriodal coordinates eta, xi, phi with solutions PSI = S(h, eta)R(h, eta) Phi(phi) and Psi = S(ih, eta)R(ih,--ieta)Phi(phi), respectively. Here h=kd/2, where d is the interfocal diatance. A Fortran computer program called ANGLFN has been devised to evaluate numerically the angle solutions S(h, eta and S(ih, eta. The printed output from ANFLFN consists of angle functions of the first kind, S(1)(h, eta) and S(1)(ih, eta, and their first and second derivatives with respect to eta. This report first describes the input data cards and the output format. The theory of the spheroidal wave functions is then discussed. A description of the principal internal features of ANGLFN is then given. Finally, a computer listing of ANGLFN is attached as an appendix. (Author)

Descriptors :   (*SPECIAL FUNCTIONS(MATHEMATICAL), NUMERICAL ANALYSIS), DIFFERENTIAL EQUATIONS, MATRICES(MATHEMATICS), WAVE FUNCTIONS, SERIES(MATHEMATICS), APPROXIMATION(MATHEMATICS), COMPUTER PROGRAMS

Subject Categories : Theoretical Mathematics
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE