WOLFRAM SYSTEM MODELER

LambertW

Closed approximation of Lambert's w function for solving f(x) = x exp(x) for x

Wolfram Language

In[1]:=
SystemModel["Modelica.Fluid.Dissipation.Utilities.Functions.General.LambertW"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

This function calculates an approximation of the inverse for 

f(x) = y = x * exp( x )

within ∞ > y > -1/e. The relative deviation of this approximation for Lambert's w function x = W(y) is displayed in the following graph.

LambertW_deviation

For y > 10 and higher values the relative deviation is smaller 2%.

Syntax

x = LambertW(y)

Inputs (1)

y

Type: Real

Description: Input f(x)

Outputs (1)

x

Type: Real

Description: Output W(y)