Wright omega function

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

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

It is simpler to be defined by its inverse function

${\displaystyle z(\omega )=\ln(\omega )+\omega }$