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4
Elementary Functions
Logarithm, Exponential, Powers
4.3
Graphics
4.3
Graphics
4.4
Special Values and Limits
Figure 4.3.2
(See
in context
.)
(i)
z
-plane
(ii)
w
-plane
A
B
C
C
¯
D
D
¯
E
E
¯
F
z
0
r
r
+
i
π
r
−
i
π
i
π
−
i
π
−
r
+
i
π
−
r
−
i
π
−
r
w
1
e
r
−
e
r
+
i
0
−
e
r
−
i
0
−
1
+
i
0
−
1
−
i
0
−
e
−
r
+
i
0
−
e
−
r
−
i
0
e
−
r
Figure 4.3.2:
Conformal mapping of exponential and logarithm.
w
=
e
z
,
z
=
ln
w
.
ⓘ
Annotations:
Symbols:
π
: the ratio of the circumference of a circle to its diameter
,
z
¯
: complex conjugate
,
e
: base of natural logarithm
,
i
: imaginary unit
,
ln
z
: principal branch of logarithm function
,
z
: complex variable
,
w
: mapping
and
r
: real parameter
Permalink:
http://dlmf.nist.gov/4.3.F2.mag
Encodings:
Magnified png
,
pdf
See also:
Annotations for
§4.3
and
Ch.4