Perturbed Padé approximation with high accuracy

摘要

In this paper, we introduce a perturbed Padé approximation of a function f(x) which has a convergent power series. This approximation depends on a perturbation parameter. This parameter is calculated so that the perturbed approximation agrees with the approximant power series to a certain order through the unit interval [0,1]. The accuracy of the introduced approximation increases as the order increases. Also, perturbed Padé approximation of the derivatives of a function are derived directly without any change of the perturbation parameter. Finally, perturbed Padé approximations of some functions and their derivatives are given.