An Elementary Treatment of the Lambert-W Relation

Abstract

Summary In this discussion, we introduced the Lambert-W relation, how to solve equations that are solvable via this relation and not solvable otherwise, discussed how to numerically calculate values, how to generate the real and imaginary parts of W for which have sufficiently negative or complex arguments. We then gave a brief insight into one of the physical applications of the Lambert-W relation that is used in fluid mechanics. Although one could introduce several new functions into the algebraic toolbox for those exploring mathematics, we have demonstrated that the Lambert-W relation is one that can easily be adapted into the toolbox of elementary-level mathematics students.