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NIST
33
Coulomb Functions
Variables
r
,
ϵ
33.14
Definitions and Basic Properties
33.16
Connection Formulas
§33.15
Graphics
ⓘ
Keywords:
Coulomb functions: variables
r
,
ϵ
,
graphics
Permalink:
http://dlmf.nist.gov/33.15
See also:
Annotations for
Ch.33
Contents
§33.15(i)
Line Graphs of the Coulomb Functions
f
(
ϵ
,
ℓ
;
r
)
and
h
(
ϵ
,
ℓ
;
r
)
§33.15(ii)
Surfaces of the Coulomb Functions
f
(
ϵ
,
ℓ
;
r
)
,
h
(
ϵ
,
ℓ
;
r
)
,
s
(
ϵ
,
ℓ
;
r
)
, and
c
(
ϵ
,
ℓ
;
r
)
§33.15(i)
Line Graphs of the Coulomb Functions
f
(
ϵ
,
ℓ
;
r
)
and
h
(
ϵ
,
ℓ
;
r
)
ⓘ
Notes:
These graphs were produced at NIST.
Permalink:
http://dlmf.nist.gov/33.15.i
See also:
Annotations for
§33.15
and
Ch.33
Figure 33.15.1:
f
(
ϵ
,
ℓ
;
r
)
,
h
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
0
,
ϵ
=
4
.
Magnify
ⓘ
Symbols:
f
(
ϵ
,
ℓ
;
r
)
: regular Coulomb function
,
h
(
ϵ
,
ℓ
;
r
)
: irregular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F1
Encodings:
pdf
,
png
See also:
Annotations for
§33.15(i)
,
§33.15
and
Ch.33
Figure 33.15.2:
f
(
ϵ
,
ℓ
;
r
)
,
h
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
1
,
ϵ
=
4
.
Magnify
ⓘ
Symbols:
f
(
ϵ
,
ℓ
;
r
)
: regular Coulomb function
,
h
(
ϵ
,
ℓ
;
r
)
: irregular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F2
Encodings:
pdf
,
png
See also:
Annotations for
§33.15(i)
,
§33.15
and
Ch.33
Figure 33.15.3:
f
(
ϵ
,
ℓ
;
r
)
,
h
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
0
,
ϵ
=
-
1
/
ν
2
,
ν
=
1.5
.
Magnify
ⓘ
Symbols:
f
(
ϵ
,
ℓ
;
r
)
: regular Coulomb function
,
h
(
ϵ
,
ℓ
;
r
)
: irregular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F3
Encodings:
pdf
,
png
See also:
Annotations for
§33.15(i)
,
§33.15
and
Ch.33
Figure 33.15.4:
f
(
ϵ
,
ℓ
;
r
)
,
h
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
0
,
ϵ
=
-
1
/
ν
2
,
ν
=
2
.
Magnify
ⓘ
Symbols:
f
(
ϵ
,
ℓ
;
r
)
: regular Coulomb function
,
h
(
ϵ
,
ℓ
;
r
)
: irregular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F4
Encodings:
pdf
,
png
See also:
Annotations for
§33.15(i)
,
§33.15
and
Ch.33
Figure 33.15.5:
f
(
ϵ
,
ℓ
;
r
)
,
h
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
0
,
ϵ
=
-
1
/
ν
2
,
ν
=
2.5
.
Magnify
ⓘ
Symbols:
f
(
ϵ
,
ℓ
;
r
)
: regular Coulomb function
,
h
(
ϵ
,
ℓ
;
r
)
: irregular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F5
Encodings:
pdf
,
png
See also:
Annotations for
§33.15(i)
,
§33.15
and
Ch.33
§33.15(ii)
Surfaces of the Coulomb Functions
f
(
ϵ
,
ℓ
;
r
)
,
h
(
ϵ
,
ℓ
;
r
)
,
s
(
ϵ
,
ℓ
;
r
)
, and
c
(
ϵ
,
ℓ
;
r
)
ⓘ
Keywords:
Coulomb functions: variables
r
,
ϵ
,
graphics
Notes:
These surfaces were produced at NIST.
Permalink:
http://dlmf.nist.gov/33.15.ii
See also:
Annotations for
§33.15
and
Ch.33
Figure 33.15.6:
f
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
0
,
-
2
<
ϵ
<
2
,
-
15
<
r
<
15
.
Magnify
3D
Help
ⓘ
Symbols:
f
(
ϵ
,
ℓ
;
r
)
: regular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F6
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§33.15(ii)
,
§33.15
and
Ch.33
Figure 33.15.7:
h
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
0
,
-
2
<
ϵ
<
2
,
-
15
<
r
<
15
.
Magnify
3D
Help
ⓘ
Symbols:
h
(
ϵ
,
ℓ
;
r
)
: irregular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F7
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§33.15(ii)
,
§33.15
and
Ch.33
Figure 33.15.8:
f
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
1
,
-
2
<
ϵ
<
2
,
-
15
<
r
<
15
.
Magnify
3D
Help
ⓘ
Symbols:
f
(
ϵ
,
ℓ
;
r
)
: regular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F8
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§33.15(ii)
,
§33.15
and
Ch.33
Figure 33.15.9:
h
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
1
,
-
2
<
ϵ
<
2
,
-
15
<
r
<
15
.
Magnify
3D
Help
ⓘ
Symbols:
h
(
ϵ
,
ℓ
;
r
)
: irregular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F9
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§33.15(ii)
,
§33.15
and
Ch.33
Figure 33.15.10:
s
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
0
,
-
0.15
<
ϵ
<
0.10
,
0
<
r
<
65
.
Magnify
3D
Help
ⓘ
Symbols:
s
(
ϵ
,
ℓ
;
r
)
: regular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F10
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§33.15(ii)
,
§33.15
and
Ch.33
Figure 33.15.11:
c
(
ϵ
,
ℓ
;
r
)
with
ℓ
=
0
,
-
0.15
<
ϵ
<
0.10
,
0
<
r
<
65
.
Magnify
3D
Help
ⓘ
Symbols:
c
(
ϵ
,
ℓ
;
r
)
: irregular Coulomb function
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F11
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
§33.15(ii)
,
§33.15
and
Ch.33