ABSTRACT
This chapter discusses the fundamental solution to Laplace’s equation in unbounded space. It discusses polynomial solutions of Laplace’s equation. A symmetrical tensor has six independent components but because of the constraint that the tensor satisfies Laplace’s equation, it must be traceless, leaving but five independent components. The chapter devises a systematic and convenient way to generate the spherical harmonics as functions of the spherical angles and employs a convenient form of a Taylor expansion. It discusses orthonormality condition and Legendre’s polynomials.
