Relationship between Inverse Langevin Function and r0-r1-Lambert W Function

Abstract

The relationship between the inverse Langevin function and the proposed r0-r1-Lambert W function is defined. The derived relationship leads to new approximations for the inverse Langevin function with lower relative error bounds than comparable published approximations. High accuracy approximations, based on Schröder’s root approximations of the first kind, are detailed. Several applications are detailed.