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ProductLog

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

ProductLog[z]
    gives the principal solution w of z == w e^w (the Lambert W function).
ProductLog[k, z] gives the k-th solution (k any integer, k == 0 the
principal branch); branches are ordered by imaginary part. ProductLog[z]
is real for z >= -1/e and has a branch cut along (-Infinity, -1/e].
Exact values include ProductLog[0] = 0, ProductLog[-1/E] = -1,
ProductLog[E] = 1, ProductLog[-Pi/2] = I Pi/2 and ProductLog[k, 0] =
-Infinity for k != 0. Inexact real or complex arguments evaluate
numerically at machine or arbitrary (MPFR) precision. Satisfies
D[ProductLog[z], z] = ProductLog[z]/(z (1 + ProductLog[z])). Listable.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= ProductLog[1.0]
Out[1]= 0.567143

In[2]:= ProductLog[-1/E]
Out[2]= -1

Implementation notes

Attributes: Listable, NumericFunction, Protected, ReadProtected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References