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      Power Series.Orthogonal Operational Expansions

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            Abstract

            Formulation of the classic Taylor series as an orthogonal concept based on identifying the expansions coefficients as differential transformation applied to a unique function; definition of operational orthogonality by analogy with the Hilbert space and identification of the nth derivative at a point based on the improper integral on the positive semiaxis ; deduction of inversion integrals for Laplace transforms for analytical functions

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            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            16 October 2020
            Affiliations
            [1 ] Mathematic Professor , Holguin Univ
            Author information
            https://orcid.org/0000-0001-7189-5452
            Article
            10.14293/S2199-1006.1.SOR-.PPK4CQC.v1
            258efcc3-1db2-4468-af8f-6fb04660db68

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            History
            : 16 October 2020

            All data generated or analysed during this study are included in this published article (and its supplementary information files).
            Analysis,Applied mathematics
            orthogonal operational, operational space,power serie,Laguerre polynomials,Hermite polynomials,Laplace inversion

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