Vitalii S. Shpakivskyi, Tetyana S. Kuzmenko, Quaternionic G-Monogenic Mappings in Em, Volume 12, International Journal of Advanced Research in Mathematics (Volume 12)
https://www.scipress.com/IJARM.12.1
Abstract:
    We consider a class of so-called quaternionic G-monogenic mappings associatedwith m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of allmappings from this class by using four analytic functions of complex variable. For G-monogenicmappings we generalize some analogues of classical integral theorems of the holomorphic functiontheory of the complex variable (the surface and the curvilinear Cauchy integral theorems,the Cauchy integral formula, the Morera theorem), and Taylor’s and Laurent’s expansions.Moreover, we investigated the relation between G-monogenic and H-monogenic (differentiablein the sense of Hausdorff) quaternionic mappings.
Keywords:
    Complex Quaternions Algebra, Constructive Description, Gateaux Derivative, G-Monogenic Mappings, H-Monogenic Mappings, Integral Theorems, Singular Points, Taylor’s and Laurent’s Expansions