Single-layer density as function of Stokes' constants

Summary A relation between Stokes' constants (harmonic coefficients) J _n ^(k) , S _n ^(k) has been derived in the development for the external geopotential and the coefficients in the development for the single-layer density distributed over the surface of the external ellipsoid, the external equipotential surface, as well as the smoothed physical surface of the actual Earth. Terms of the 2nd order, (J ₂ ⁽⁰⁾ ) ² , were taken into account, terms of the 3rd and lower orders were neglected.