Wright omega function

Summary

The Wright omega function $\omega$ is a single-valued function built from the branches of the Lambert W function. It is $\omega(z) = W_{K(z)}(e^z)$, where the unwinding number $K(z)$ picks the branch. It solves the equation $\omega + \ln \omega = z$ for all $z$ off two horizontal half-lines. On the real line it is the unique real solution of this equation. It is convenient in computer algebra because it avoids the choice of a branch.