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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
          Article
          10.14293/S2199-1006.1.SOR-.PPK4CQC.v1

          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 .

          All data generated or analysed during this study are included in this published article (and its supplementary information files).

          Analysis, Applied mathematics

          orthogonal operational, Laplace inversion, Hermite polynomials, Laguerre polynomials, power serie, operational space

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