On Monogenic Series Expansions with Applications to Linear Elasticity

Abstract

In this paper recently studied orthogonal Appell bases of solid spherical monogenics in \({\mathbb{R}^3}\) are used to construct a polynomial basis of solutions to the Lame equation from linear elasticity. To this end, a compact closed form representation of the Appell basis elements in terms of classical spherical harmonics is proved and a recently developed spatial generalization of the Kolosov-Muskhelishvili formulae in terms of a monogenic and an anti-monogenic function is applied.