Accession Number : AD0666919

Title :   CERTAIN NUMERICAL PROPERTIES OF THE LEGENDRE FUNCTION AND THE ASSOCIATED LEGENDRE FUNCTION,

Corporate Author : AEROSPACE CORP SAN BERNARDINO CALIF SAN BERNARDINO OPERATIONS

Personal Author(s) : Jorgensen,P. S.

Report Date : MAR 1968

Pagination or Media Count : 16

Abstract : The Legendre function and the associated Legendre function are orthogonal sets of functions, i.e., the integral of the square of a normalized function is unity and the integral of any pair of functions of different degree is zero. This will be only approximately true when ideal integration is replaced by a simple numerical summation. In doing this, certain curious numerical properties have been observed which are discussed by a few illustrative examples. The practical implication of these numerical aspects of the Legendre function, when performing harmonic analysis in spherical coordinates, is discussed. (Author)

Descriptors :   (*SPECIAL FUNCTIONS(MATHEMATICAL), NUMERICAL METHODS AND PROCEDURES), HARMONIC ANALYSIS, INTEGRAL EQUATIONS, BOUNDARY VALUE PROBLEMS, SPHERES, GRAVITY, EARTH(PLANET)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE