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6
Exponential, Logarithmic, Sine, and
Cosine Integrals
Properties
6.10
Other Series Expansions
6.12
Asymptotic Expansions
§6.11
Relations to Other Functions
ⓘ
Notes:
For (
6.11.1
) and (
6.11.2
) see
Temme (
1996b
, pp. 180 and 187)
. For (
6.11.3
) use (
6.5.7
).
Permalink:
http://dlmf.nist.gov/6.11
See also:
Annotations for
Ch.6
For the notation see §§
8.2(i)
and
13.2(i)
.
Incomplete Gamma Function
ⓘ
Keywords:
exponential integrals
,
incomplete gamma function
,
incomplete gamma functions
,
relations to other functions
See also:
Annotations for
§6.11
and
Ch.6
6.11.1
E
1
(
z
)
=
Γ
(
0
,
z
)
.
ⓘ
Symbols:
E
1
(
z
)
: exponential integral
,
Γ
(
a
,
z
)
: incomplete gamma function
and
z
: complex variable
A&S Ref:
5.1.45
(special case of)
Referenced by:
§6.11
Permalink:
http://dlmf.nist.gov/6.11.E1
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
§6.11
,
§6.11
and
Ch.6
Confluent Hypergeometric Function
ⓘ
Keywords:
auxiliary functions for sine and cosine integrals
,
confluent hypergeometric functions
,
exponential integrals
,
relation to confluent hypergeometric functions
,
relations to other functions
,
sine and cosine integrals
See also:
Annotations for
§6.11
and
Ch.6
6.11.2
E
1
(
z
)
=
e
−
z
U
(
1
,
1
,
z
)
,
ⓘ
Symbols:
U
(
a
,
b
,
z
)
: Kummer confluent hypergeometric function
,
e
: base of natural logarithm
,
E
1
(
z
)
: exponential integral
and
z
: complex variable
Referenced by:
§6.11
,
5th item
,
§6.6
Permalink:
http://dlmf.nist.gov/6.11.E2
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
§6.11
,
§6.11
and
Ch.6
6.11.3
g
(
z
)
+
i
f
(
z
)
=
U
(
1
,
1
,
−
i
z
)
.
ⓘ
Symbols:
U
(
a
,
b
,
z
)
: Kummer confluent hypergeometric function
,
i
: imaginary unit
,
f
(
z
)
: auxiliary function for sine and cosine integrals
,
g
(
z
)
: auxiliary function for sine and cosine integrals
and
z
: complex variable
Referenced by:
§6.11
,
5th item
Permalink:
http://dlmf.nist.gov/6.11.E3
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
§6.11
,
§6.11
and
Ch.6