Analytical approximations to the Lambert W function

The Lambert W function is defined as the multivalued inverse of the function w -> we(w). It has a wide range of applications. We propose a new method to construct a high-precision analytical approximation of the two branches of W . The method is based on Pade approx-imation and Schroder's iteration. This method can also be extended to solve other tran-scendental equations in science and engineering. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

The Lambert W function, which is a multivalued inverse function, has various applications. A new method based on Pade approximation and Schroder's iteration is proposed to construct a high-precision analytical approximation for the two branches of the W function. This method can also be extended to solve other transcendental equations in science and engineering.