Perihelion precession in non-Newtonian central potentials

High order corrections to the perihelion precession are obtained in non-Newtonian central potentials, via complex analysis techniques. The result is an exact series expansion whose terms, for a perturbation of the form $\delta V=\frac{\gamma}{r^{s}}$, are calculated in closed form. To validate the method, the series is applied to the specific case of s=3, and the results are compared with those presented in literature, which are relate to the Schwarzschild metric. As a further test, a numerical simulation was carried out for the case where s=4. The algebraic calculations and numerical simulations were carried out via software with symbolic capabilities.