In this paper, it is revealed that Adomian decomposition method corresponds to Taylor series method when applied to the solution of nonlinear initial value problems, in the following sense: the Adomian ́s polynomials can be obtain trough Taylor coefficients.

A point mass at the center of an ellipsoidal homogeneous fluid is used as a simple model to study the effect of rotation on the shape and external gravitational field of planets and stars. Maclaurin’s analytical result for a homogenous body is generalized to this model. The absence of a third order term in the Taylor expansion of the Maclaurin function leads to further simple but very accurate ...

An algorithm for obtaining the Taylor coefficients of an expansion of Feynman diagrams is proposed. It is based on recurrence relations which can be applied to the propagator as well as to the vertex diagrams. As an application, several coefficients of the Taylor series expansion for the two-loop non-planar vertex and two-loop propagator diagrams are calculated. The results of the numerical eva...

Abstract In this paper, by virtue of the symmetry principle, applying techniques real analysis and Euler–Maclaurin summation formula, we construct proper weight coefficients use them to establish a reverse extended Hardy–Hilbert’s inequality with multi-parameters. Then, obtain equivalent forms some statements best possible constant factor related several parameters. Finally, illustrate how obta...

We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also obtain solutions to certain systems of Volterra equations of the first kind. In all cases except the case of logarithmic singularities, we obtain recursive fo...