Constructive description of monogenic functions in a finite-dimensional   commutative associative algebra
  Let $\mathbb{A}_n^m$ be an arbitrary $n$-dimensional commutative associative algebra over the field of complex numbers with $m$ idempotents. Let $e_1=1,e_2,e_3$ be elements of $\mathbb{A}_n^m$ 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 $xe_1+ye_2+ze_3$ 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. 
Vitalii Shpakivskyi
math.AC