Laguerre derivative and monogenic Laguerre polynomials: An operational approach

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 con...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 53; no. 5-6; pp. 1084 - 1094
Main Authors: Cação, I., Falcão, M.I., Malonek, H.R.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.03.2011
Elsevier
Subjects:
computer techniques
decision making
Exact sciences and technology
Exponential operators
Functions of a complex variable
Functions of hypercomplex variables
Generalized Laguerre polynomials
Mathematical analysis
mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Sciences and techniques of general use
Several complex variables and analytic spaces
Special functions
Exponential operators
Generalized Laguerre polynomials
Functions of hypercomplex variables
Applied mathematics
One variable function
Harmonic analysis
Laguerre polynomial
Mathematical model
Computer aided analysis
Complex variable function
ISSN:0895-7177, 1872-9479
Online Access:Get full text
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Summary: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.
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ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2010.11.071