Abstract
This chapter focuses on the harmonic polynomials and spherical functions. It presents definition of spherical functions and approximation by means of spherical harmonics. It reviews that an arbitrary continuous function can be represented on a sphere of unit radius by a linear combination of the functions of orders 0, 1, …, N with any desired accuracy provided N is sufficiently large. An arbitrary function F(θ, ϕ), which is continuous on the sphere of unit radius, can be represented thereon with any desired accuracy in the form of a polynomials.
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