Generalizing Taylor Expansion Series Through Succeeding Initial Value Problems

• M. Fernández-Martínez ^[2] ; J. L. G. Guirao ^[1]
  1. [1] Universidad Politécnica de Cartagena

     Universidad Politécnica de Cartagena

     Cartagena, España

     
  2. [2] Centro Universitario de la Defensa
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 1, 2017, págs. 71-100
• Idioma: inglés
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• Resumen

  • In this paper, the classical Taylor’s expansion series for a given continuous and k-times differentiable real function is obtained as the unique solution of a certain class of initial value problems. Further, through some subsequent generalizations regarding that problem in terms of certain derivative-based operators, we obtain some generalized Taylor’s type polynomial expansions, including the Taylor–Aleph series, which remains as particular cases. In addition to that, some analytical properties about these involved operators are also provided.