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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
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
Figure 6.3.1:
The exponential integrals
${E}_{1}\left(x\right)$
and
$\mathrm{Ei}\left(x\right)$
,
$$
.
Symbols:
${E}_{1}\left(z\right)$
: exponential integral
,
$\mathrm{Ei}\left(x\right)$
: exponential integral
and
$x$
: real variable
Keywords:
exponential integrals
Permalink:
http://dlmf.nist.gov/6.3.F1
Encodings:
pdf
,
png
Figure 6.3.2:
The sine and cosine integrals
$\mathrm{Si}\left(x\right),\mathrm{Ci}\left(x\right)$
,
$0\le x\le 15$
.
Symbols:
$\mathrm{Ci}\left(z\right)$
: cosine integral
,
$\mathrm{Si}\left(z\right)$
: sine integral
and
$x$
: real variable
Keywords:
cosine integrals
,
sine integrals
Referenced by:
§6.16(i)
Permalink:
http://dlmf.nist.gov/6.3.F2
Encodings:
pdf
,
png
For a graph of
$\mathrm{li}\left(x\right)$
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
Visualization Help
Figure 6.3.3:
$|{E}_{1}\left(x+\mathrm{i}y\right)|$
,
$-4\le x\le 4$
,
$-4\le y\le 4$
. Principal value. There is a cut along the negative real axis. Also,
$|{E}_{1}\left(z\right)|\to \mathrm{\infty}$
logarithmically as
$z\to 0$
.
Symbols:
${E}_{1}\left(z\right)$
: exponential integral
,
$x$
: real variable
and
$z$
: complex variable
Keywords:
exponential integrals
Permalink:
http://dlmf.nist.gov/6.3.F3
Encodings:
VRML
,
X3D
,
pdf
,
png