Laguerre derivative and monogenic Laguerre polynomials: An operational approach

Authors:
I. CaçãO;M. I. FalcãO;H. R. Malonek
Affiliations:
Department of Mathematics, University of Aveiro, Portugal;Department of Mathematics and Applications, University of Minho, Portugal;Department of Mathematics, University of Aveiro, Portugal
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

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Abstract

Hypercomplex function theory generalizes the theory of holomorphic functions of one complex variable by using Clifford Algebras and provides the fundamentals of Clifford Analysis as a refinement of Harmonic Analysis in higher dimensions. We define the Laguerre derivative operator in hypercomplex context and by using operational techniques we construct generalized hypercomplex monogenic Laguerre polynomials. Moreover, Laguerre-type exponentials of order m are defined.