On the Accuracy of the Coefficients in a Series of Spherical Harmonics

摘要

The accuracy of the coefficients of a development in a series of spherical harmonics is investigated. Usually the coefficients are determined by numerical integration. Therefore, the surface of the sphere is divided into small surface elements and the mean value of the function for each surface element is estimated. Two sources of error are distinguished: (1) Representation error. This is the error of the estimation of the mean value of the function for each surface element. (2) Integration error. This is the error caused by the replacement of the integral by a numerical integration. Both errors are separately investigated. (Author)