The flow function of the liquid outside the particle was derived from the ellipsoid harmonics function.

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.