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

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). y = ω(z) is the unique solution, when for x ≤ −1, of the equation y + ln(y) = z. Except for those two values, the Wright omega function is continuous, even analytic.

Properties

The Wright omega function satisfies the relation. It also satisfies the differential equation wherever ω is analytic (as can be seen by performing separation of variables and recovering the equation ), and as a consequence its integral can be expressed as: Its Taylor series around the point takes the form : where in which is a second-order Eulerian number.

Values

Plots