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4
Elementary Functions
Logarithm, Exponential, Powers
4.13
Lambert
W
-Function
4.13
Lambert
W
-Function
4.14
Definitions and Periodicity
Figure 4.13.2
(See
in context
.)
Figure 4.13.2:
The
W
(
z
)
function on the first 5 Riemann sheets.
W
(
z
)
maps the first Riemann sheet
|
ph
(
z
+
e
−
1
)
|
<
π
in the middle of the left-hand side to the region enclosed by the green curve on the right-hand side; it maps the Riemann sheet
π
<
ph
z
<
3
π
on the left-hand side to the region enclosed by the pink, green and orange curves on the right-hand side, etc.
ⓘ
Annotations:
Symbols:
W
(
z
)
: Lambert
W
-function
,
π
: the ratio of the circumference of a circle to its diameter
,
e
: base of natural logarithm
,
ph
: phase
and
z
: complex variable
Keywords:
Lambert
W
-function
,
branch cuts
Permalink:
http://dlmf.nist.gov/4.13.F2.mag
Encodings:
Magnified png
,
pdf
Addition (effective with 1.1.7):
This figure was added.
See also:
Annotations for
§4.13
and
Ch.4