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On a generalized Appell system and monogenic power series
Author(s) -
Bock S.,
Gürlebeck K.
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1213
Subject(s) - mathematics , hypercomplex number , series (stratigraphy) , appell series , taylor series , pure mathematics , power series , generating function , space (punctuation) , dirichlet series , algebra over a field , integrable system , orthogonal polynomials , quaternion , dirichlet distribution , mathematical analysis , hypergeometric function , geometry , generalized hypergeometric function , paleontology , hypergeometric function of a matrix argument , linguistics , philosophy , boundary value problem , biology
Recently Appell systems of monogenic polynomials in ℝ 3 were constructed by several authors. Main purpose of this paper is the description of another Appell system that is complete in the space of square integrable quaternion‐valued functions. A new Taylor‐type series expansion based on the Appell polynomials is presented, which can be related to the corresponding Fourier series analogously as in the complex one‐dimensional case. These results find applications in the description of the hypercomplex derivative, the monogenic primitive of a monogenic function and the characterization of functions from the monogenic Dirichlet space. Copyright © 2009 John Wiley & Sons, Ltd.