Biaxial monogenic functions from Funk‐Hecke's formula combined with Fueter's theorem

Abstract

Funk‐Hecke's formula allows a passage from plane waves to radially invariant functions. It may be adapted to transform axial monogenics into biaxial monogenics that are monogenic functions invariant under the product group SO(p)× SO(q). Fueter's theorem transforms holomorphic functions in the plane into axial monogenics, so that by combining both results, we obtain a method to construct biaxial monogenics from holomorphic functions.