# scipy.special.wrightomega¶

scipy.special.wrightomega(z, out=None) = <ufunc 'wrightomega'>

Wright Omega function.

Defined as the solution to

$\omega + \log(\omega) = z$

where $$\log$$ is the principal branch of the complex logarithm.

Parameters: z : array_like Points at which to evaluate the Wright Omega function omega : ndarray Values of the Wright Omega function

lambertw
The Lambert W function

Notes

New in version 0.19.0.

The function can also be defined as

$\omega(z) = W_{K(z)}(e^z)$

where $$K(z) = \lceil (\Im(z) - \pi)/(2\pi) \rceil$$ is the unwinding number and $$W$$ is the Lambert W function.

The implementation here is taken from [1].

References

 [1] (1, 2) Lawrence, Corless, and Jeffrey, “Algorithm 917: Complex Double-Precision Evaluation of the Wright $$\omega$$ Function.” ACM Transactions on Mathematical Software, 2012. DOI:10.1145/2168773.2168779.