On the calculation of monogenic primitives. (English) Zbl 1208.30047

Summary: The theory of functions with values in the algebra of quaternions shows a lot of analogies to the function theory in the complex one-dimensional case. The class of holomorphic functions is replaced by the set of null solutions of a generalized Cauchy-Riemann system, the class of monogenic functions. R. Delanghe described in [Complex Var. Elliptic Equ. 51, No. 8–11, 959–970 (2006; Zbl 1121.30023)] the basic ideas of an algorithm to construct monogenic primitives of the Fueter polynomials. Main goal of this paper is to complete the proposed algorithm for the anti-derivation and to calculate the primitives explicitly.


30G35 Functions of hypercomplex variables and generalized variables


Zbl 1121.30023
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