An application of the multivariate Lagrange-Bürmann expansion in mathematical geodesy

Abstract

In the simplified model of geodesy where the earth is conceived as a rotational ellipsoid, if the eccentricity of the ellipsoid is to be determined from gravity measurements, an equation of the form y = x − z h ( x ) y = x - zh\left ( x \right ) is to be solved for x x , where y y and z z are small parameters whose values can be measured and h h is a known function. We obtain the expansion of x x in powers of y y and z z by means of the general Lagrange—Bürmann formula.