Expressions for Analytical Transformation Between Gauss and Mercator Projections by Complex Numbers

Expressions for the forward and inverse solution of Gauss and Mercator projections by complex numbers are given in this paper.Based on these expressions,direct and indirect formulas of the analytical transformation between Gauss and Mercator projections are derived.These formulae are symbolical forms which include the first eccentricity e of the reference ellipsoide.Hence,they can solve problems that deal with transformations between Gauss and Mercator projections when different reference ellipsoids are used.The numerical investigation shows that these formulas are sufficiently accurate up to 0.000 1 m and can satisfy practical applications.