A novel rational padé approximation of the inverse Langevin function

Inverse of the Langevin function has many applicationsspecially in polymer elasticity and smart magneto/electrostrictivestructures. There is no explicit analyticrepresentation for this function, so many approximationfunctions have been established in the literature. In thepresent paper, the rational padé approximation is used inconjunction with a multi-point collocation method to reach anovel function, which match well the main inverse Langevinfunction for both negative and positive values. A simplerapproximation function is also derived using the chebyshevpolynomials and the idea of series economization. It hasbeen shown that the presented formula has a maximum errorof 1% which is less than the other approximations in theliterature.