In this paper,the basic theory of spherical cap harmonic (SCH) analysismethod is induced and the relationship between the SCH coefficients and the wave lengthof the gravity field is discussed.

This paper involves the use of the spherical harmonic function in molecular surface simulation to resolve the problem of docking between macromolecules (proteins) and make a stable foundation for the computer aided drug design.

To study the effect of gravity eccentricity on the ranges,the expression of gravity was educed using spherical harmonic function when the earth is considered as an normal ellipsoid or sphere.

Using spherical harmonic function expansion and finite element method,Boltzmann transport equation is solved numerically,the convergence of the method is approved.

The computation on a sort of integrals of the product of spherical harmonics and trigonometric functions;

Secondorder boundary perturbation theory was used to develop a fully 3D electrostatic potential analysis of a halfbowl spherical rotor balance device to derive the electrostatic field disturbance torque equation which was described by spherical harmonics.

Using the properties of the harmonic function and the theories of the expansion of the spherical harmonics,the equivalence between Moritz analytical continuation and Bjerhammar s virtual spherical solution is proved according to the power series expanded form of the real number field function,the differences in meaning between the two solutions are analyzed.

The characters of several current calculation methods of disturbing gravitation are compared and the spherical harmonics function to calculate the disturbing gravitation is adopted.

The spherical harmonic series expressions of electromagnetic fields excited by ELF/SLF horizontal electric dipole in spherical Earth-ionosphere guide when earth and ionosphere are regarded as the imperfectly electric conductor has been derived.

In this paper, the spherical harmonic series expressions of electromagnetic fields excited by ELF/SLF vertical electric dipole in spherical Earth-ionosphere guide taken earth and ionosphere as the imperfectly electric conductor are derived, and a method to speed numerical convergence is presented.

By finite approximation method, the following results are obtained: the solution can be transformed into a linear system of the coefficients of spherical harmonic series if the continent is considered as a spherical cap.