Power series representation for monogenic functions in based on a permutational product

On Generalized Hypercomplex Laguerre-Type Exponentials and Applications

“…In Clifford Analysis, several different methods have been developed for constructing monogenic functions as series with respect to properly chosen homogeneous monogenic polynomials (see [1,3,4,5,11,14,17,18]). …”

“…It is also the reason why in the polynomial approximation in the context of Clifford Analysis almost every problem needs the development of different adapted polynomial bases (e.g. [1,3,4,5,11,18]). …”

Laguerre Polynomials in Several Hypercomplex Variables and Their Matrix Representation

“…Therefore they can be used as basis for generalized power series. Following [11] and [12] it has been shown that the multiple power series of the form…”

“…, x n ). In [11] has been shown that the partial derivatives of z σ with respect to x k are obtained as…”

“…The paper is organized as follows. In Section 2.1 , we briefly recall some concepts of Clifford Algebras in higher dimensional Euclidean vector spaces (for details see [6], [10], [11], [12]). After that, in Section 2.2, generalized multivariate Laguerre polynomials are introduced.…”