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NIST
6
Exponential, Logarithmic, Sine, and
Cosine Integrals
Properties
6.2
Definitions and Interrelations
6.4
Analytic Continuation
§6.3
Graphics
ⓘ
Permalink:
http://dlmf.nist.gov/6.3
See also:
Annotations for
Ch.6
Contents
§6.3(i)
Real Variable
§6.3(ii)
Complex Variable
§6.3(i)
Real Variable
ⓘ
Notes:
These graphs were produced at NIST.
Permalink:
http://dlmf.nist.gov/6.3.i
See also:
Annotations for
§6.3
and
Ch.6
Figure 6.3.1:
The exponential integrals
E
1
(
x
)
and
Ei
(
x
)
,
0
<
x
≤
2
.
Magnify
ⓘ
Symbols:
E
1
(
z
)
: exponential integral
,
Ei
(
x
)
: exponential integral
and
x
: real variable
Keywords:
exponential integrals
,
graphics
Permalink:
http://dlmf.nist.gov/6.3.F1
Encodings:
pdf
,
png
See also:
Annotations for
§6.3(i)
,
§6.3
and
Ch.6
Figure 6.3.2:
The sine and cosine integrals
Si
(
x
)
,
Ci
(
x
)
,
0
≤
x
≤
15
.
Magnify
ⓘ
Symbols:
Ci
(
z
)
: cosine integral
,
Si
(
z
)
: sine integral
and
x
: real variable
Keywords:
cosine integrals
,
graphics
,
sine integrals
Referenced by:
§6.16(i)
Permalink:
http://dlmf.nist.gov/6.3.F2
Encodings:
pdf
,
png
See also:
Annotations for
§6.3(i)
,
§6.3
and
Ch.6
For a graph of
li
(
x
)
see Figure
6.16.2
.
§6.3(ii)
Complex Variable
ⓘ
Notes:
This surface was produced at NIST.
Permalink:
http://dlmf.nist.gov/6.3.ii
See also:
Annotations for
§6.3
and
Ch.6
Figure 6.3.3:
|
E
1
(
x
+
i
y
)
|
,
-
4
≤
x
≤
4
,
-
4
≤
y
≤
4
. Principal value. There is a cut along the negative real axis. Also,
|
E
1
(
z
)
|
→
∞
logarithmically as
z
→
0
.
Magnify
3D
Help
ⓘ
Symbols:
E
1
(
z
)
: exponential integral
,
i
: imaginary unit
,
x
: real variable
and
z
: complex variable
Keywords:
exponential integrals
,
graphics
Permalink:
http://dlmf.nist.gov/6.3.F3
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§6.3(ii)
,
§6.3
and
Ch.6