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Laguerre derivative and monogenic Laguerre polynomials: An operational approach

Laguerre derivative and monogenic Laguerre polynomials: An operational approach,10.1016/j.mcm.2010.11.071,Mathematical and Computer Modelling,Isabel C

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Laguerre derivative and monogenic Laguerre polynomials: An operational approach   (Citations: 3)
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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.
Journal: Mathematical and Computer Modelling - MATH COMPUT MODELLING , vol. 53, no. 5-6, pp. 1084-1094, 2011
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    • ...Ca¸ c˜ ao et al. ([3]) used an operational approach, introducing a hypercomplex Laguerre derivative operator, to construct monogenic Laguerre polynomials that generalize the ordinary Laguerre polynomials in the real and one complex variable cases to the multivariate case...

    H. R. Malonek, et al. Laguerre Polynomials in Several Hypercomplex Variables and Their Matri...

    • ...[1, 4, 5, 11, 14, 17]) allowed, for instance, to develop new hypercomplex analytic tools for linking Clifford Analysis with operational approaches to special classes of monogenic hypercomplex polynomials or even to combinatorics...
    • ...Following [4] we introduce now the main results concerning Appell sequences...
    • ...Theorem 1 ([4], Theorem 1). A monogenic polynomial sequence (Fk) k≥0 is an Appell set if and only if it satisfies the binomial-type identity...
    • ...In the recent paper [4], adapting the aforementioned operational approach, we have introduced the definition of hypercomplex Laguerre derivative operator...
    • ...Remark 2. In [4], we have defined monogenic Laguerre polynomials in R n+1 , which were obtained by applying the exponential operator Exp n (−LD )t o the sequence (1Q n (−x)) k≥0 ...

    I. Cação, et al. On Generalized Hypercomplex Laguerre-Type Exponentials and Application...

    • ...A similar operational approach was already considered in [5] to obtain monogenic generalized Laguerre polynomials...
    • ...Using equality (4), the binomial-type formula for this Appell sequence (see [5]) can be written as...

    I. Cação, et al. On an Hypercomplex Generalization of Gould-Hopper and Related Chebyshe...

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