`wrightOmega`

Wright omega function, the solution of w + log(w) = z.

Category: Mathematics > Mathematical Functions

Syntax

w = wrightOmega(z)

Returns the value w that satisfies w + log(w) = z.

Description

The Wright omega function is related to the Lambert W function by omega(z) = W(exp(z)) for z with imaginary part in a suitable strip, so for real z it is lambertw(exp(z)). It is real and positive for real z, and it satisfies omega(1) = 1 and omega(z) + log(omega(z)) = z.

It is better suited than lambertw(exp(z)) for large z, where exp(z) would overflow.

Input arguments

z: Real or complex scalar or array.

Output arguments

w: Values of the Wright omega function, with the size of z.

Example

Check the defining equation

w = wrightOmega([0 1 3])
w + log(w)

Output

w = 1×3

    0.5671    1.0000    2.2079
ans = 1×3

   -0.0000    1.0000    3.0000

wrightOmega