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NIST
33
Coulomb Functions
Variables
r
,
ϵ
33.17
Recurrence Relations and Derivatives
33.19
Power-Series Expansions in
r
§33.18
Limiting Forms for Large
ℓ
ⓘ
Keywords:
Coulomb functions: variables
r
,
ϵ
,
limiting forms for large
ℓ
Notes:
Combine (
33.5.8
) and (
33.16.1
), (
33.16.2
). For
f
(
ϵ
,
ℓ
;
r
)
(
33.19.1
) can also be used.
Referenced by:
§33.23(iv)
Permalink:
http://dlmf.nist.gov/33.18
See also:
Annotations for
Ch.33
As
ℓ
→
∞
with
ϵ
and
r
(
≠
0
) fixed,
33.18.1
f
(
ϵ
,
ℓ
;
r
)
∼
(
2
r
)
ℓ
+
1
(
2
ℓ
+
1
)
!
,
h
(
ϵ
,
ℓ
;
r
)
∼
(
2
ℓ
)
!
π
(
2
r
)
ℓ
.
ⓘ
Symbols:
f
(
ϵ
,
ℓ
;
r
)
: regular Coulomb function
,
h
(
ϵ
,
ℓ
;
r
)
: irregular Coulomb function
,
∼
: asymptotic equality
,
π
: the ratio of the circumference of a circle to its diameter
,
!
: factorial (as in
n
!
)
,
ℓ
: nonnegative integer
,
r
: real variable
and
ϵ
: real parameter
Permalink:
http://dlmf.nist.gov/33.18.E1
Encodings:
TeX
,
TeX
,
pMML
,
pMML
,
png
,
png
See also:
Annotations for
§33.18
and
Ch.33