The Cauchy-Pompeiu integral formula in elliptic complex numbers

Abstract: The aim of this article is to give a generalization of the Cauchy-Pompeiu integral formula for functions valued in parameter-depending elliptic algebras with structure polynomial $X^2 + \beta X + \alpha$ where $\alpha$ and $\beta$ are real numbers. As a consequence, a Cauchy integral representation formula is obtained for a generalized class of holomorphic functions.