Accession Number : AD0602787

Title :   FINAL REPORT. THEORY OF SPHEROIDAL FUNCTIONS ,

Corporate Author : MICHIGAN UNIV ANN ARBOR RADIATION LAB

Personal Author(s) : Sleator,Frederick B.

Report Date : JUN 1964

Pagination or Media Count : 11

Abstract : The objective of this investigation, as well as an earlier one, AD-400 968, was to develop and exploit new relations between the spheroidal functions and other better known functions which might reduce the labor and complication involved in obtaining new numerical values of the spheroidal functions and thus facilitate the quantitative solutions of new spheroidal diffraction problems or the extension of existing solutions into ranges not previously covered. An adequate assessment of the forms and methods described in the discussion will depend, of course, on some fairly voluminous computations, as well as some more detailed analytical work. Preferably these two lines of advance should be closely coordinated and the overall direction should be determined in accordance with the requirements of the unsolved or only partly solved physical problems. Although the present forms should give values sufficiently accurate for practical applications, it is clear that they are more suitable for filling in gaps in existing tables as the need arises than for large-scale production of new ones. One of the principal features of the Bessel function approximation is that it exhibits the dependence of the spheroidal functions on the wavelength-eccentricity parameter c and on the eigenvalue lambda sub m n more explicitly than the usual representations. Further exploitation of this feature should be of value in a number of circumstances. (Author)

Descriptors :   (*SPECIAL FUNCTIONS (MATHEMATICAL), THEORY), ELLIPSOIDS, SPHERES, GEOMETRY, OPTICS, DIFFRACTION, SERIES(MATHEMATICS), INTEGRALS, DIFFERENTIAL EQUATIONS, MATRICES(MATHEMATICS), NUMERICAL ANALYSIS, FUNCTIONAL ANALYSIS

Distribution Statement : APPROVED FOR PUBLIC RELEASE