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LambertWWm1 Method

Computes the W_{-1} branch of the Lambert W function for real arguments in the range -1/e %le; z < 0.

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)
Syntax
C#
Copy
public static double Wm1(
	double z,
	int maxIter = 50,
	double tol = 1E-12
)

Parameters

z  Double
The input value for which to compute the W_{-1} branch. Must satisfy -1/e <= z < 0.
maxIter  Int32  (Optional)
The maximum number of iterations to use when refining the result. Must be positive. The default is 50.
tol  Double  (Optional)
The convergence tolerance for the iterative solver. Must be positive. The default is 1e-12.

Return Value

Double
The value w such that w ⋅ e^{w} = z, where w is on the W_{-1} branch. Returns a real number for valid z in the range -1/e <= z < 0.
Exceptions
ExceptionCondition
ArgumentOutOfRangeExceptionThrown when z is outside the valid range of -1/e <= z < 0.
Remarks
The W_{-1} branch of the Lambert W function is defined only for real z in the interval -1/e <= z < 0. This method uses an iterative approach and may not converge for values of z very close to -1/e or for insufficiently large maxIter or loose tol values.
See Also