SciPy

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

Returns:
omega : ndarray

Values of the Wright Omega function

See also

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.

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