This paper made use of the MATLAB to plot spatial distribution of spherical function,pointed out the software of MATLAB is a valid tool to visualization of equation of mathematical physics.

The solution of spherical function is given in the paper,and it is applied reasonably in the problem of eigenvalue of angular momentum square operator.

Basing on summable method of classical function s Fourier series,a genernal spherical functions summability theorem of spherical functions on SL(2,R) is presnented by using the convolution of approximation indential kernel with funtions and the spherical function expansion formula.

In this paper, applying Life theory of complex-functional, not only the space harmonic functions in polynomial form but also the spherical functions are obtained.

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.

There,norm is Holder norm of spherical function.

In this paper,four spherical functions based on 3D model geometry features was defined,each spherical function describe 3D model from a certain point of view.