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Title: Monogenic pseudo-complex power functions and their applications
Author: Cruz, Carla
Falcão, Maria Irene
Malonek, Helmuth R.
Keywords: Functions of hypercomplex variables
Combinatorial identities
Generalized Appell polynomials
Issue Date: Aug-2014
Publisher: John Wiley & Sons
Abstract: The use of a non-commutative algebra in hypercomplex function theory requires a large variety of different representations of polynomials suitably adapted to the solution of different concrete problems. Naturally arises the question of their relationships and the advantages or disadvantages of different types of polynomials. In this sense, the present paper investigates the intrinsic relationship between two different types of monogenic Appell polynomials. Several authors payed attention to the construction of complete sets of monogenic Appell polynomials, orthogonal with respect to a certain inner product, and used them advantageously for the study of problems in 3D-elasticity and other problems. Our goal is to show that, as consequence of the binomial nature of those generalized Appell polynomials, their inner structure is determined by interesting combinatorial relations in which the central binomial coefficients play a special role. As a byproduct of own interest, a Riordan-Sofo type binomial identity is also proved.
Peer review: yes
DOI: 10.1002/mma.2931
ISSN: 1099-1476
Appears in Collections:CIDMA - Artigos

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