On generalized derivatives and formal powers for pseudoanalytic functions

  • Peter Berglez Graz University of Technology
Keywords: Pseudoanalytic functions, Generalized (F, G)-derivative, Formal powers


We consider pseudoanalytic functions depending on two or three real variables. They are characterized by the corresponding Bers-Vekua equations. In the case of two dimensions we use the complex notation whereas for the case of three variables the concept of complex quaternions serves for our investigations. In a particular plane case we give an explicit representation of formal powers with which a complete system of solutions of the corresponding Bers-Vekua equation can be given. By an example we show how the concept of formal powers may also be applied to the case of three variables.

Author Biography

Peter Berglez, Graz University of Technology
Department of Mathematics
Graz University of Technology, Austria