Shifted Appell sequences in Clifford analysis

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 a parts per thousand yen 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 . In particular, we construct an explicit sequence for the case being an arbitrary homogeneous monogenic polynomial defined in . The connection of this sequence with the so-called Fueter's theorem will also be discussed