The extension of a functional equation of the Lambert W function

Abstract

The principal branch of the Lambert W function satisfies a well-known functional equation with respect to the sum of two of its values, but this equation is valid only on a restricted set. In this paper, we extend this equation to all the branches of W and to the arbitrary complex linear combination of two values. The results give an application for the unwinding number, too.

Keywords:

• Lambert W function
• functional equation
• unwinding number
• branches

AMS CLASSIFICATION:

• 33E99

Acknowledgments

The author would like to thank to the unknown referee for his/her comments. These helped to clarify the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).