Wright Omega function
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, as the only solution is given by z = e−ω.
y = ω is the unique solution, when for x ≤ −1, of the equation y + ln = z. Except on those two rays, 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, 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
