On a class of functions defined by partial differential equations

whose real and imaginary parts are connected by the equations (1.1). Many concepts and results in the theory of analytic functions of a complex variable can be extended to functions satisfying the system (1.1), notably the concept of differentiation, integration, powers, power series, the theorem of Cauchy and Morera and the fundamental theorem of algebra('). In what follows we make the following assumptions concerning the coefficients <r,-, Tj.