Wright omega function
In mathematics, the Wright omega function or Wright function, denoted ω, is defined in terms of the Lambert W function as: ω ( z ) = W ⌈ I m ( z ) − π 2 π ⌉ ( e z ) . {\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 z ( ω ) = ln ( ω ) + ω {\displaystyle z(\omega )=\ln(\omega )+\omega } == Uses == One of the main applications of this function is in the resolution of the equation z = ln(z), as the only solution is given by z = e−ω(π i).