DLMF
Index
Notations
Search
Help?
Citing
Customize
Annotate
UnAnnotate
About the Project
NIST
11
Struve and Related Functions
Struve and Modified Struve Functions
11.2
Definitions
11.4
Basic Properties
§11.3
Graphics
ⓘ
Permalink:
http://dlmf.nist.gov/11.3
See also:
Annotations for
Ch.11
Contents
§11.3(i)
Struve Functions
§11.3(ii)
Modified Struve Functions
§11.3(i)
Struve Functions
ⓘ
Notes:
These graphics were produced at NIST.
Permalink:
http://dlmf.nist.gov/11.3.i
See also:
Annotations for
§11.3
and
Ch.11
Figure 11.3.1:
H
ν
(
x
)
for
0
≤
x
≤
12
and
ν
=
0
,
1
2
,
1
,
3
2
,
2
,
3
.
Magnify
ⓘ
Symbols:
H
ν
(
z
)
: Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F1
Encodings:
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.2:
K
ν
(
x
)
for
0
<
x
≤
16
and
ν
=
0
,
1
2
,
1
,
3
2
,
2
,
3
.
Magnify
ⓘ
Symbols:
K
ν
(
z
)
: Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F2
Encodings:
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.3:
H
ν
(
x
)
for
0
≤
x
≤
12
and
ν
=
-
3
,
-
2
,
-
3
2
,
-
1
,
-
1
2
.
Magnify
ⓘ
Symbols:
H
ν
(
z
)
: Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F3
Encodings:
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.4:
K
ν
(
x
)
for
0
<
x
≤
16
and
ν
=
-
4
,
-
3
,
-
2
,
-
1
,
0
. If
ν
=
-
1
2
,
-
3
2
, …, then
K
ν
(
x
)
is identically zero.
Magnify
ⓘ
Symbols:
K
ν
(
z
)
: Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F4
Encodings:
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.5:
H
ν
(
x
)
for
0
≤
x
≤
8
and
-
4
≤
ν
≤
4
.
Magnify
3D
Help
ⓘ
Symbols:
H
ν
(
z
)
: Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F5
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.6:
K
ν
(
x
)
for
0
≤
x
≤
8
and
-
4
≤
ν
≤
4
.
Magnify
3D
Help
ⓘ
Symbols:
K
ν
(
z
)
: Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F6
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.7:
|
H
0
(
x
+
i
y
)
|
for
-
8
≤
x
≤
8
and
-
3
≤
y
≤
3
.
Magnify
3D
Help
ⓘ
Symbols:
H
ν
(
z
)
: Struve function
,
i
: imaginary unit
and
x
: real variable
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F7
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.8:
|
K
0
(
x
+
i
y
)
|
(principal value) for
-
8
≤
x
≤
8
and
-
3
≤
y
≤
3
. There is a cut along the negative real axis.
Magnify
3D
Help
ⓘ
Symbols:
K
ν
(
z
)
: Struve function
,
i
: imaginary unit
and
x
: real variable
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F8
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.9:
|
H
1
2
(
x
+
i
y
)
|
(principal value) for
-
8
≤
x
≤
8
and
-
3
≤
y
≤
3
. There is a cut along the negative real axis.
Magnify
3D
Help
ⓘ
Symbols:
H
ν
(
z
)
: Struve function
,
i
: imaginary unit
and
x
: real variable
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F9
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.10:
|
K
1
2
(
x
+
i
y
)
|
(principal value) for
-
8
≤
x
≤
8
and
-
3
≤
y
≤
3
. There is a cut along the negative real axis.
Magnify
3D
Help
ⓘ
Symbols:
K
ν
(
z
)
: Struve function
,
i
: imaginary unit
and
x
: real variable
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F10
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.11:
|
H
1
(
x
+
i
y
)
|
for
-
8.5
≤
x
≤
8.5
and
-
3
≤
y
≤
3
.
Magnify
3D
Help
ⓘ
Symbols:
H
ν
(
z
)
: Struve function
,
i
: imaginary unit
and
x
: real variable
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F11
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
Figure 11.3.12:
|
K
1
(
x
+
i
y
)
|
(principal value) for
-
8
≤
x
≤
8
and
-
3
≤
y
≤
3
. There is a cut along the negative real axis.
Magnify
3D
Help
ⓘ
Symbols:
K
ν
(
z
)
: Struve function
,
i
: imaginary unit
and
x
: real variable
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F12
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(i)
,
§11.3
and
Ch.11
§11.3(ii)
Modified Struve Functions
ⓘ
Notes:
These graphics were produced at NIST.
Permalink:
http://dlmf.nist.gov/11.3.ii
See also:
Annotations for
§11.3
and
Ch.11
Figure 11.3.13:
L
ν
(
x
)
for
0
≤
x
<
4.38
and
ν
=
0
,
1
2
,
1
,
3
2
,
2
,
3
.
Magnify
ⓘ
Symbols:
L
ν
(
z
)
: modified Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F13
Encodings:
pdf
,
png
See also:
Annotations for
§11.3(ii)
,
§11.3
and
Ch.11
Figure 11.3.14:
M
ν
(
x
)
for
0
≤
x
≤
16
and
ν
=
0
,
1
2
,
1
,
3
2
,
2
,
3
.
Magnify
ⓘ
Symbols:
M
ν
(
z
)
: modified Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F14
Encodings:
pdf
,
png
See also:
Annotations for
§11.3(ii)
,
§11.3
and
Ch.11
Figure 11.3.15:
L
ν
(
x
)
for
0
≤
x
<
4.25
and
ν
=
-
3
,
-
2
,
-
3
2
,
-
1
,
-
1
2
.
Magnify
ⓘ
Symbols:
L
ν
(
z
)
: modified Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F15
Encodings:
pdf
,
png
See also:
Annotations for
§11.3(ii)
,
§11.3
and
Ch.11
Figure 11.3.16:
M
ν
(
x
)
for
0
<
x
≤
16
and
ν
=
-
3
,
-
2
,
-
3
2
,
-
1
,
-
1
2
.
Magnify
ⓘ
Symbols:
M
ν
(
z
)
: modified Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F16
Encodings:
pdf
,
png
See also:
Annotations for
§11.3(ii)
,
§11.3
and
Ch.11
Figure 11.3.17:
L
ν
(
x
)
for
0
≤
x
≤
5.6
and
-
4
≤
ν
≤
4
.
Magnify
3D
Help
ⓘ
Symbols:
L
ν
(
z
)
: modified Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F17
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(ii)
,
§11.3
and
Ch.11
Figure 11.3.18:
M
ν
(
x
)
for
0
≤
x
≤
8
and
-
4
≤
ν
≤
4
.
Magnify
3D
Help
ⓘ
Symbols:
M
ν
(
z
)
: modified Struve function
,
x
: real variable
and
ν
: real or complex order
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F18
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(ii)
,
§11.3
and
Ch.11
Figure 11.3.19:
|
M
-
1
2
(
x
+
i
y
)
|
(principal value) for
-
3
≤
x
≤
3
and
-
3
≤
y
≤
3
. There is a cut along the negative real axis.
Magnify
3D
Help
ⓘ
Symbols:
M
ν
(
z
)
: modified Struve function
,
i
: imaginary unit
and
x
: real variable
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F19
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(ii)
,
§11.3
and
Ch.11
Figure 11.3.20:
|
M
1
2
(
x
+
i
y
)
|
(principal value) for
-
3
≤
x
≤
3
and
-
3
≤
y
≤
3
. There is a cut along the negative real axis.
Magnify
3D
Help
ⓘ
Symbols:
M
ν
(
z
)
: modified Struve function
,
i
: imaginary unit
and
x
: real variable
Keywords:
Struve functions and modified Struve functions
,
graphics
Permalink:
http://dlmf.nist.gov/11.3.F20
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§11.3(ii)
,
§11.3
and
Ch.11