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On a generalized Appell system and monogenic power series. (English) Zbl 1195.30068

Appell systems of monogenic polynomials in \(\mathbb R^3\) were recently constructed by several authors. The primary purpose of this paper is to describe another Appell system that is complete in the space of square integrable, quaternion-valued functions. The authors provide a new Taylor-type series expansion based on Appell polynomials. The authors’ results find applications to the characterization of the hypercomplex derivative, to the monogenic primitive of a monogenic function, and to functions in the monogenic Dirichlet space.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
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