Wright omega function

The Wright omega function along part of the real axis

In mathematics, the Wright omega function or Wright function, denoted ω, is defined in terms of the Lambert W function as:

$\omega (z)=W_{{\big \lceil }{\frac {\mathrm {Im} (z)-\pi }{2\pi }}{\big \rceil }}(e^{z}).$

It is simpler to be defined by its inverse function

$z(\omega )=\ln(\omega )+\omega$