Title: On the role of hypergeometric functions in Dirac type equations Authors: Cacao, Isabel ×Constales, DenisKrausshar, Rolf Sören # Issue Date: 2007 Publisher: Springer New York LLC Host Document: AIP Conference Proceedings vol:936 pages:726-729 Abstract: Let $D :=\sum_{i=1}^n \frac{\partial }{\partial x_i} e_i$ be the Euclidean Dirac operator in the $n$-dimensional flat space $\mathbb{R}^{n}$, ${\bf E}:=\sum_{i=1}^n x_i \frac{\partial }{\partial x_i}$ the radial symmetric Euler operator and $\alpha$ and $\lambda$ be arbitrary non-zero complex parameters. In this paper we use hypercomplex analysis methods to treat the PDE systems $[D - \lambda - \alpha {\bf E}]f = 0$ and $[D - \lambda - \alpha {\bf x}{\bf E}]f = 0$. We give an explicit description of the solutions in terms of hypergeometric functions and special homogeneous monogenic polynomials. ISSN: 0094-243X Publication status: published KU Leuven publication type: IC Appears in Collections: Analysis Section