A Simplification of the Meridian Formula and Its Taylor-series Interpretation

A more concise formula of the meridian arc length was obtained by introduced two new parameters:the third flattening and the Gauss hypergeometric function.From another perspective,the simplified formula is also can be explained by a Taylor series expansion.By this,we got error estimate of the formula in terms of the Lagrange form of the remainder.For numerical verification of the error estimate theory,application example was presented by using the WGS84data.The results show that experimental data are consistent with the error estimate theory and the simplified formula is more precise than the standard one.