ABSTRACT
The famous Legendre functions are widely used in the sciences; in particular, they serve as a set of basis functions for the Fourier expansion of solutions of many physical problems in spherical coordinates. As we see in this chapter, problems with spherical symmetry, such as vibrating spheres, spherical charge distributions, and the quantum probability distribution of an electron trapped in the spherical potential of an atom, in general lead to Legendre functions. We discuss the origin of the Legendre functions, their properties, and several applications.
