On paravector valued homogeneous monogenic polynomials with binomial expansion
type: Item
instance of: scholarly article
title: On paravector valued homogeneous monogenic polynomials with binomial expansion
zbMATH Open document ID: 1264.30038
published in: Advances in Applied Clifford Algebras
publication date: 2013-01-10T00:00:00Z
full work available at URL: http://hdl.handle.net/1822/20135
review text: Starting from a set of paravector valued homogeneous monogenic polynomials the authors construct a sequence of generalized Appell polynomials. Two different types of polynomials are studied. One of them is given by (analogous to the complex powers \(z^k\)) \[ {\mathcal P}^k(x_0,\widehat x)= (x_0+ (i_1 x_1+ i_2x_2)(i_1 e_1+ i_2 e_2))^k. \] This generation of polynomials is an alternative to the Fueter-Sce construction (only for odd integer dimension) and the Cauchy-Kovalevskaya extension. The proofs are lined out in the case \(n=2\). An important role plays the constant imaginary vector \[ \widehat i= (i_1 e_1+\cdots+ i_n e_n) \] with \(\widehat i^2=-1\), i.e., \(\widehat i\) is a generalized unit vector.
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 6123928
zbMATH Keywords: Clifford analysis
zbMATH Keywords: generalized Appell polynomial
author: Helmuth R. Malonek
author: Maria Irene Falcão
MaRDI profile type: Publication
OpenAlex ID: W1994213639
Wikidata QID: Q58197874
cites work: On a generalized Appell system and monogenic power series
cites work: Laguerre derivative and monogenic Laguerre polynomials: an operational approach
cites work: Polynomials satisfying a binomial theorem
cites work: Generalized Exponentials through Appell sets in R[sup n+1] and Bessel functions
cites work: Analytische Funktionen einer Quaternionenvariablen
cites work: A hypercomplex derivative of monogenic functsions in and its Applications
cites work: On Appell sets and the Fueter-Sce mapping
cites work: Canonical bases for \(\mathfrak {sl}(2,\mathbb {C})\)-modules of spherical monogenics in dimension 3.
cites work: Holomorphic Cliffordian functions
cites work: Modified quaternionic analysis in
cites work: A new hypercomplex structure of the euclidean space R m+1 and the concept of hypercomplex differentiability
cites work: Q4831680
cites work: A note on a generalized Joukowski transformation
cites work: Special Monogenic Polynomials—Properties and Applications
cites work: Generalization of the Cauchy-Riemann Equations and Representations of the Rotation Group
DOI: 10.1007/S00006-012-0361-5
description: scientific article; zbMATH DE number 6123928