2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64937We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as criteria for functions of a quaternion variable to be analytic. In particular, the quaternionic exponential and logarithmic functions are being considered. Main results include quaternion versions of Hurwitz' theorem, Mittag-Leffler's theorem and Weierstrass theorem.48 pages, LatexComplex Variables30C99 (Primary), 12E15, 30E20 (Secondary)text