Generalizing Taylor Expansion Series Through Succeeding Initial Value Problems

Área de investigación: Applied Mathematics Año: 2017
Tipo de publicación: Artículo Palabras clave: Initial value problem; Taylor expansion series; Laplace transform
Autores: Fernández Martínez, Manuel; Guirao, J. L. G.
Journal: Qualitative Theory of Dynamical Systems Volumen: 16
Número: 1 Páginas: 71-100
Mes: April
ISSN: 1575-5460
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.