## On representation of the internal spherical functions and their derivatives in the planetary coordinate system

The expressions of spherical functions and their derivatives in a Cartesian coordinate system are obtained. In opposite to the representation of polynomials in a spherical coordinate system, the derived recurrence relations make it possible to use them in the description of physical processes, and the obtained formulae for derivatives of spherical functions within the sphere allow obtaining the solutions to the problems of mathematical physics for spherical bodies in a Cartesian coordinate system. This approach has its advantages precisely in the applied problems. For example, for the d