Comment on ‘Improving series convergence: The simple pendulum and beyond’ - Fernández, Francisco Marcelo (2021)
In this comment we analyze the improved series proposed by Duki et al (2018 Eur. J. Phys. 39 065802) for the approximate calculation of a variety of physical quantities like the period of the simple pendulum and an integral of the exponential of a two-dimensional potential-energy function. We show that the application of the approach to the latter case is unnecessary because both the expansion coefficients and the original problem are given in terms of a similar error function. Present results for the straightforward expansion with exact analytic coefficients do not show the oscillatory behaviour exhibited by the calculations of those authors. We give reasons why the improved approach of Duki et al may not be suitable for the treatment of many realistic physical problems.