On the Role of Hypergeometric Functions in Dirac Type Equations

Abstract

Let D: = Σi = 1n∂∂xiei be the Euclidean Dirac operator in the n‐dimensional flat space Rn, E: = Σi = 1nxi∂∂xi the radial symmetric Euler operator and α and λ be arbitrary non‐zero complex parameters. In this paper we use hypercomplex analysis methods to treat the PDE systems [D−λ−αE]f = 0 and [D−λ−αxE]f = 0. We give an explicit description of the solutions in terms of hypergeometric functions and special homogeneous monogenic polynomials.