Comments on an Orthogonal Family of Monogenic Functions on Spheroidal Domains

Abstract

The problem of building an orthogonal basis for the space of square-integrable harmonic functions defined in a spheroidal (either oblate or prolate) domain leads to special functions, which provide an elegant analysis of a variety of physical problems. Many generalizations of these ideas in the context of Quaternionic Analysis possess a similar elegant mathematical structure. A brief descriptive review is given of these developments.