Computational Methods and Function Theory 12 (2012), No. 2, 371--391
Copyright Heldermann Verlag 2012
Isabel Cação
isabel.cacao@ua.pt , University of Aveiro, Department of Mathematics, Center for Research and Development in Mathematics and Applications, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.
Maria Irene Falcão
mif@math.uminho.pt , University of Aveiro, Center for Research and Development in Mathematics and Applications, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.
Helmuth R. Malonek
hrmalon@ua.pt , University of Aveiro, Department of Mathematics, Center for Research and Development in Mathematics and Applications, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.
This paper provides an insight into different structures of a special polynomial sequence of binomial type in higher dimensions with values in a Clifford algebra. The elements of the special polynomial sequence are homogeneous hypercomplex differentiable (monogenic) functions of different degrees and their matrix representation allows for their recursive construction in the same way as for complex power functions. This property can somehow be considered as a compensation for the loss of multiplicativity caused by the non-commutativity of the underlying algebra.
Keywords: Special polynomial sequence, monogenic function, matrix representation.
MSC 2000: Primary 47A56; Secondary 30G35, 33C50.
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