A matrix approach to families of Appell polynomial sequences: The hypercomplex case
Helmuth R. Malonek1, Graça Tomaz2
1University of Aveiro, Portugal; 2Polytechnic Institute of Guarda, Portugal
It is well known that classical univariate Appell polynomial sequences have a wide range of applications in several areas of mathematics, but also in physics, chemistry, and engineering. This fact justified the recent development of a matrix approach [Aceto, Tomaz, Malonek] as an easy and comprehensible tool, also for non-mathematicians. Moreover, by using recent results about families of sequences of orthogonal hyperholomorphic homogenous Appell polynomial [Cação, Falcão, Malonek] this approach leads to generalizations in the framework of Clifford Analysis. The aim of the paper is to show, that in the real as well as hypercomplex case, the arithmetical origins are based on the simple structure of a so-called creation matrix, the related Pascal matrix, and some universal coefficient sequence of real numbers.
ISSN 1611 - 4086 | © IKM 2015