Removal of Singularities from Taylor Series

A mathematical procedure is described whereby the radius of convergence of a Taylor series can be increased through the inclusion of complex poles in a rational approximation. Computer results show that this technique is quite independent of the asymptotic limit of the power series and only depends on the positions of the singularities. Aside from the applications in one variable, this method vastly improves perturbative solutions to symplectic, dynamical mappings in many dimensions by removing resonances in the complex plane