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33
Coulomb Functions
Variables
r
,
Ο΅
33.16
Connection Formulas
33.18
Limiting Forms for Large
β
Β§33.17
Recurrence Relations and Derivatives
β
Keywords:
Coulomb functions: variables
r
,
Ο΅
,
derivatives
,
recurrence relations
Notes:
See
Seaton (
2002a
, Eqs. 77, 78, 82)
.
Referenced by:
Β§33.23(iv)
,
Β§33.23(iv)
Permalink:
http://dlmf.nist.gov/33.17
See also:
Annotations for
Ch.33
33.17.1
(
β
+
1
)
β’
r
β’
f
β‘
(
Ο΅
,
β
β
1
;
r
)
β
(
2
β’
β
+
1
)
β’
(
β
β’
(
β
+
1
)
β
r
)
β’
f
β‘
(
Ο΅
,
β
;
r
)
+
β
β’
(
1
+
(
β
+
1
)
2
β’
Ο΅
)
β’
r
β’
f
β‘
(
Ο΅
,
β
+
1
;
r
)
=
0
,
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/33.17.E1
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
Β§33.17
and
Ch.33
33.17.2
(
β
+
1
)
β’
(
1
+
β
2
β’
Ο΅
)
β’
r
β’
h
β‘
(
Ο΅
,
β
β
1
;
r
)
β
(
2
β’
β
+
1
)
β’
(
β
β’
(
β
+
1
)
β
r
)
β’
h
β‘
(
Ο΅
,
β
;
r
)
+
β
β’
r
β’
h
β‘
(
Ο΅
,
β
+
1
;
r
)
=
0
,
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/33.17.E2
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
Β§33.17
and
Ch.33
33.17.3
(
β
+
1
)
β’
r
β’
f
β²
β‘
(
Ο΅
,
β
;
r
)
=
(
(
β
+
1
)
2
β
r
)
β’
f
β‘
(
Ο΅
,
β
;
r
)
β
(
1
+
(
β
+
1
)
2
β’
Ο΅
)
β’
r
β’
f
β‘
(
Ο΅
,
β
+
1
;
r
)
,
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/33.17.E3
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
Β§33.17
and
Ch.33
33.17.4
(
β
+
1
)
β’
r
β’
h
β²
β‘
(
Ο΅
,
β
;
r
)
=
(
(
β
+
1
)
2
β
r
)
β’
h
β‘
(
Ο΅
,
β
;
r
)
β
r
β’
h
β‘
(
Ο΅
,
β
+
1
;
r
)
.
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/33.17.E4
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
Β§33.17
and
Ch.33