A novel rational padé approximation of the inverse Langevin function

Inverse of the Langevin function has many applications specially in polymer elasticity and smart magneto/electro-strictive structures. There is no explicit analytic representation for this function, so many approximation functions have been established in the literature. In the present paper, the rational padé approximation is used in conjunction with a multi-point collocation method to reach a novel function, which match well the main inverse Langevin function for both negative and positive values. A simpler approximation function is also derived using the chebyshev polynomials and the idea of series economization. It has been shown that the presented formula has a maximum