2024/02/13 by Michael Parfenov, Parfenov, Michael · 1 citation
Mathematics · #30G35 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Mathematics and Applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2402.08487
openalex publication_date 2024/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class of introduced H-holomorphic functions consists of those quaternionic functions whose left and right derivatives become equal after the transition to 3D space. The presented theory demonstrates a complete similarity of the algebraic properties and differentiation rules between the classes of H-holomorphic and ordinary complex holomorphic functions, including the fact that quaternionic multiplication of the H-holomorphic functions behaves as commutative and the fact that each H-holomorphic function can be created from its complex holomorphic analogue by replacing a complex variable by a quaternion one. A fairly large number of detailed examples are given to illustrate the presented theory efficiency.