Accurate approximants of inverse Brillouin functions

We present an investigation to improve the polynomial part of an analytical approximation of inverse Brillouin functions, recently proposed in the literature. For the analytical approximation, we employ a sextic polynomial model. To determine the best fit coefficients of the model, we apply a simple statistical analysis. We obtained the same accuracy as the only case presented in the literature, but with three orders of magnitude fewer points involved in the statistical analysis, which translates into a faster convergence of the coefficients. We extend the investigation to the most interesting cases for physical applications. The method can be applied to any other desired inverse Brillouin functions or polynomial approximations of special functions.