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

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 $y = x - zh\left ( x \right )$ is to be solved for $x$, where $y$ and $z$ are small parameters whose values can be measured and $h$ is a known function. We obtain the expansion of $x$ in powers of $y$ and $z$ by means of the general Lagrange—Bürmann formula.