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NIST
10
Bessel Functions
Spherical Bessel Functions
10.47
Definitions and Basic Properties
10.49
Explicit Formulas
§10.48
Graphs
ⓘ
Keywords:
graphs
,
spherical Bessel functions
Notes:
These graphs were produced at NIST.
Permalink:
http://dlmf.nist.gov/10.48
See also:
Annotations for
Ch.10
Figure 10.48.1:
j
n
(
x
)
,
n
=
0
(
1
)
4
,
0
≤
x
≤
12
.
Magnify
ⓘ
Symbols:
j
n
(
z
)
: spherical Bessel function of the first kind
,
n
: integer
and
x
: real variable
Permalink:
http://dlmf.nist.gov/10.48.F1
Encodings:
pdf
,
png
See also:
Annotations for
§10.48
and
Ch.10
Figure 10.48.2:
y
n
(
x
)
,
n
=
0
(
1
)
4
,
0
<
x
≤
12
.
Magnify
ⓘ
Symbols:
y
n
(
z
)
: spherical Bessel function of the second kind
,
n
: integer
and
x
: real variable
Permalink:
http://dlmf.nist.gov/10.48.F2
Encodings:
pdf
,
png
See also:
Annotations for
§10.48
and
Ch.10
Figure 10.48.3:
j
5
(
x
)
,
y
5
(
x
)
,
j
5
2
(
x
)
+
y
5
2
(
x
)
,
0
≤
x
≤
12
.
Magnify
ⓘ
Symbols:
j
n
(
z
)
: spherical Bessel function of the first kind
,
y
n
(
z
)
: spherical Bessel function of the second kind
and
x
: real variable
Permalink:
http://dlmf.nist.gov/10.48.F3
Encodings:
pdf
,
png
See also:
Annotations for
§10.48
and
Ch.10
Figure 10.48.4:
j
5
′
(
x
)
,
y
5
′
(
x
)
,
j
5
′
2
(
x
)
+
y
5
′
2
(
x
)
,
0
≤
x
≤
12
.
Magnify
ⓘ
Symbols:
j
n
(
z
)
: spherical Bessel function of the first kind
,
y
n
(
z
)
: spherical Bessel function of the second kind
and
x
: real variable
Permalink:
http://dlmf.nist.gov/10.48.F4
Encodings:
pdf
,
png
See also:
Annotations for
§10.48
and
Ch.10
Figure 10.48.5:
i
0
(
1
)
(
x
)
,
i
0
(
2
)
(
x
)
,
k
0
(
x
)
,
0
≤
x
≤
4
.
Magnify
ⓘ
Symbols:
i
n
(
1
)
(
z
)
: modified spherical Bessel function
,
i
n
(
2
)
(
z
)
: modified spherical Bessel function
,
k
n
(
z
)
: modified spherical Bessel function
and
x
: real variable
Referenced by:
Erratum (V1.0.1) for Figure
10.48.5
Permalink:
http://dlmf.nist.gov/10.48.F5
Encodings:
pdf
,
png
Errata (effective with 1.0.1):
The ordinate labels 2 and 4 originally were misplaced at ordinates 3 and 5.
Reported 2010-11-08 by Wolfgang Ehrhardt
See also:
Annotations for
§10.48
and
Ch.10
Figure 10.48.6:
i
1
(
1
)
(
x
)
,
i
1
(
2
)
(
x
)
,
k
1
(
x
)
,
0
≤
x
≤
4
.
Magnify
ⓘ
Symbols:
i
n
(
1
)
(
z
)
: modified spherical Bessel function
,
i
n
(
2
)
(
z
)
: modified spherical Bessel function
,
k
n
(
z
)
: modified spherical Bessel function
and
x
: real variable
Permalink:
http://dlmf.nist.gov/10.48.F6
Encodings:
pdf
,
png
See also:
Annotations for
§10.48
and
Ch.10
Figure 10.48.7:
i
5
(
1
)
(
x
)
,
i
5
(
2
)
(
x
)
,
k
5
(
x
)
,
0
≤
x
≤
8
.
Magnify
ⓘ
Symbols:
i
n
(
1
)
(
z
)
: modified spherical Bessel function
,
i
n
(
2
)
(
z
)
: modified spherical Bessel function
,
k
n
(
z
)
: modified spherical Bessel function
and
x
: real variable
Permalink:
http://dlmf.nist.gov/10.48.F7
Encodings:
pdf
,
png
See also:
Annotations for
§10.48
and
Ch.10