Simple and accurate approximants of inverse Brillouin functions

•Simpler and more accurate approximants for inverse Brillouin functions are proposed.•A numerical example is worked out in detail.•The mathematics is accessible, so the paper might interest the experimentalists. A new method of obtaining accurate approximants for inverse Brillouin functions is proposed. It is based on a partial relaxation of one of the conditions recently imposed by Kröger to such approximants. The particular case of the approximant worked out in detail in this paper is with at least one order of magnitude more accurate than the approximants currently used.