Constructive description of monogenic functions in a finite-dimensional commutative associative algebra

Abstract Let 𝔸nm be an arbitrary n-dimensional commutative associative algebra over the field of complex numbers with m idempotents. Let e1 = 1, e2, e3 be elements of 𝔸nm which are linearly independent over the field of real numbers. We consider monogenic (i.e., continuous and differentiable in the sense of Gateaux) functions of the variable xe1 + ye2 + ze3, where x, y, z are real, and obtain a constructive description of all mentioned functions by means of holomorphic functions of complex variables. It follows from this description that monogenic functions have Gateaux derivatives of all orders.