c05bbc calculates an approximate value for Lambert's
function (sometimes known as the ‘product log’ or ‘Omega’ function), which is the inverse function of
The function
is many-to-one, and so, except at
,
is multivalued.
c05bbc allows you to specify the branch of
on which you would like the results to lie by using the argument
branch. Our choice of branch cuts is as in
Corless et al. (1996), and the ranges of the branches of
are summarised in
Figure 1.
For more information about the closure of each branch, which is not displayed in
Figure 1, see
Corless et al. (1996). The dotted lines in the Figure denote the asymptotic boundaries of the branches, at multiples of
.
The precise method used to approximate
is as described in
Corless et al. (1996). For
close to
greater accuracy comes from evaluating
rather than
: by setting
on entry you inform
c05bbc that you are providing
, not
, in
z.
Corless R M, Gonnet G H, Hare D E G, Jeffrey D J and Knuth D
E (1996) On the Lambert function Advances in Comp. Math. 3 329–359
For a high percentage of
,
c05bbc is accurate to the number of decimal digits of precision on the host machine (see
X02BEC). An extra digit may be lost on some platforms and for a small proportion of
. This depends on the accuracy of the base-
logarithm on your system.
Background information to multithreading can be found in the
Multithreading documentation.
The following figures show the principal branch of
.