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Shifted Appell Sequences in Clifford Analysis

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Abstract

The aim of this paper is to present a generalization of the Appell sequences within the framework of Clifford analysis called shifted Appell sequences. It consists of sequences {M n (x)} n ≥ 0 of monogenic polynomials satisfying the Appell condition (i.e. the hypercomplex derivative of each polynomial in the sequence equals, up to a multiplicative constant, its preceding term) such that the first term M 0(x) = P k (x) is a given but arbitrary monogenic polynomial of degree k defined in \({\mathbb{R}^{m+1}}\). In particular, we construct an explicit sequence for the case \({M_0(x)=\mathbf{P}_k(\underline x)}\) being an arbitrary homogeneous monogenic polynomial defined in \({\mathbb R^m}\). The connection of this sequence with the so-called Fueter’s theorem will also be discussed.

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  1. Department of Mathematics, Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193, Aveiro, Portugal

    Dixan Peña Peña

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Peña, D.P. Shifted Appell Sequences in Clifford Analysis. Results. Math. 63, 1145–1157 (2013). https://doi.org/10.1007/s00025-012-0259-5

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