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33
Coulomb Functions
Variables
r
,
Ο΅
33.14
Definitions and Basic Properties
33.16
Connection Formulas
Β§33.15
Graphics
β
Keywords:
Coulomb functions: variables
r
,
Ο΅
,
graphics
Permalink:
http://dlmf.nist.gov/33.15
See also:
Annotations for
Ch.33
Contents
Β§33.15(i)
Line Graphs of the Coulomb Functions
f
β‘
(
Ο΅
,
β
;
r
)
and
h
β‘
(
Ο΅
,
β
;
r
)
Β§33.15(ii)
Surfaces of the Coulomb Functions
f
β‘
(
Ο΅
,
β
;
r
)
,
h
β‘
(
Ο΅
,
β
;
r
)
,
s
β‘
(
Ο΅
,
β
;
r
)
, and
c
β‘
(
Ο΅
,
β
;
r
)
Β§33.15(i)
Line Graphs of the Coulomb Functions
f
β‘
(
Ο΅
,
β
;
r
)
and
h
β‘
(
Ο΅
,
β
;
r
)
β
Notes:
These graphs were produced at NIST.
Permalink:
http://dlmf.nist.gov/33.15.i
See also:
Annotations for
Β§33.15
and
Ch.33
Figure 33.15.1:
f
β‘
(
Ο΅
,
β
;
r
)
,
h
β‘
(
Ο΅
,
β
;
r
)
with
β
=
0
,
Ο΅
=
4
.
Magnify
β
Symbols:
f
β‘
(
Ο΅
,
β
;
r
)
: regular Coulomb function
,
h
β‘
(
Ο΅
,
β
;
r
)
: irregular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F1
Encodings:
pdf
,
png
See also:
Annotations for
Β§33.15(i)
,
Β§33.15
and
Ch.33
Figure 33.15.2:
f
β‘
(
Ο΅
,
β
;
r
)
,
h
β‘
(
Ο΅
,
β
;
r
)
with
β
=
1
,
Ο΅
=
4
.
Magnify
β
Symbols:
f
β‘
(
Ο΅
,
β
;
r
)
: regular Coulomb function
,
h
β‘
(
Ο΅
,
β
;
r
)
: irregular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F2
Encodings:
pdf
,
png
See also:
Annotations for
Β§33.15(i)
,
Β§33.15
and
Ch.33
Figure 33.15.3:
f
β‘
(
Ο΅
,
β
;
r
)
,
h
β‘
(
Ο΅
,
β
;
r
)
with
β
=
0
,
Ο΅
=
β
1
/
Ξ½
2
,
Ξ½
=
1.5
.
Magnify
β
Symbols:
f
β‘
(
Ο΅
,
β
;
r
)
: regular Coulomb function
,
h
β‘
(
Ο΅
,
β
;
r
)
: irregular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F3
Encodings:
pdf
,
png
See also:
Annotations for
Β§33.15(i)
,
Β§33.15
and
Ch.33
Figure 33.15.4:
f
β‘
(
Ο΅
,
β
;
r
)
,
h
β‘
(
Ο΅
,
β
;
r
)
with
β
=
0
,
Ο΅
=
β
1
/
Ξ½
2
,
Ξ½
=
2
.
Magnify
β
Symbols:
f
β‘
(
Ο΅
,
β
;
r
)
: regular Coulomb function
,
h
β‘
(
Ο΅
,
β
;
r
)
: irregular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F4
Encodings:
pdf
,
png
See also:
Annotations for
Β§33.15(i)
,
Β§33.15
and
Ch.33
Figure 33.15.5:
f
β‘
(
Ο΅
,
β
;
r
)
,
h
β‘
(
Ο΅
,
β
;
r
)
with
β
=
0
,
Ο΅
=
β
1
/
Ξ½
2
,
Ξ½
=
2.5
.
Magnify
β
Symbols:
f
β‘
(
Ο΅
,
β
;
r
)
: regular Coulomb function
,
h
β‘
(
Ο΅
,
β
;
r
)
: irregular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F5
Encodings:
pdf
,
png
See also:
Annotations for
Β§33.15(i)
,
Β§33.15
and
Ch.33
Β§33.15(ii)
Surfaces of the Coulomb Functions
f
β‘
(
Ο΅
,
β
;
r
)
,
h
β‘
(
Ο΅
,
β
;
r
)
,
s
β‘
(
Ο΅
,
β
;
r
)
, and
c
β‘
(
Ο΅
,
β
;
r
)
β
Keywords:
Coulomb functions: variables
r
,
Ο΅
,
graphics
Notes:
These surfaces were produced at NIST.
Permalink:
http://dlmf.nist.gov/33.15.ii
See also:
Annotations for
Β§33.15
and
Ch.33
Figure 33.15.6:
f
β‘
(
Ο΅
,
β
;
r
)
with
β
=
0
,
β
2
<
Ο΅
<
2
,
β
15
<
r
<
15
.
Magnify
3D
Help
β
Symbols:
f
β‘
(
Ο΅
,
β
;
r
)
: regular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F6
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
Β§33.15(ii)
,
Β§33.15
and
Ch.33
Figure 33.15.7:
h
β‘
(
Ο΅
,
β
;
r
)
with
β
=
0
,
β
2
<
Ο΅
<
2
,
β
15
<
r
<
15
.
Magnify
3D
Help
β
Symbols:
h
β‘
(
Ο΅
,
β
;
r
)
: irregular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F7
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
Β§33.15(ii)
,
Β§33.15
and
Ch.33
Figure 33.15.8:
f
β‘
(
Ο΅
,
β
;
r
)
with
β
=
1
,
β
2
<
Ο΅
<
2
,
β
15
<
r
<
15
.
Magnify
3D
Help
β
Symbols:
f
β‘
(
Ο΅
,
β
;
r
)
: regular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F8
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
Β§33.15(ii)
,
Β§33.15
and
Ch.33
Figure 33.15.9:
h
β‘
(
Ο΅
,
β
;
r
)
with
β
=
1
,
β
2
<
Ο΅
<
2
,
β
15
<
r
<
15
.
Magnify
3D
Help
β
Symbols:
h
β‘
(
Ο΅
,
β
;
r
)
: irregular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F9
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
Β§33.15(ii)
,
Β§33.15
and
Ch.33
Figure 33.15.10:
s
β‘
(
Ο΅
,
β
;
r
)
with
β
=
0
,
β
0.15
<
Ο΅
<
0.10
,
0
<
r
<
65
.
Magnify
3D
Help
β
Symbols:
s
β‘
(
Ο΅
,
β
;
r
)
: regular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F10
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
Β§33.15(ii)
,
Β§33.15
and
Ch.33
Figure 33.15.11:
c
β‘
(
Ο΅
,
β
;
r
)
with
β
=
0
,
β
0.15
<
Ο΅
<
0.10
,
0
<
r
<
65
.
Magnify
3D
Help
β
Symbols:
c
β‘
(
Ο΅
,
β
;
r
)
: irregular Coulomb function
,
β
: nonnegative integer
,
r
: real variable
and
Ο΅
: real parameter
Permalink:
http://dlmf.nist.gov/33.15.F11
Encodings:
Vizualization
,
pdf
,
png
See also:
Annotations for
Β§33.15(ii)
,
Β§33.15
and
Ch.33