The global Borel-Pompieu-type formula for quaternionic slice regular functions.

This paper presents the global Borel-Pompieu- and the global Cauchy-type integral formulas for the quaternionic slice regular functions using the relationship between this function space and a non-constant coefficient differential operator given by G := ∥ x → ∥ 2 ∂ 0 + x → ∑ k = 1 3 x k ∂ k , according to [González-Cervantes JO. On cauchy integral theorem for quaternionic slice regular functions. Complex Anal Oper Theory. 2019;13(6):2527–2539; Colombo F, González-Cervantes JO, Sabadini I. A non-constant coefficients differential operator associated to slice monogenic functions. Trans Am Math Soc. 2013;365:303–318]. This association allows to show a behavior of the theory of slice regular functions similar to the well known theories of the hypercomplex analysis. [ABSTRACT FROM AUTHOR]