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Statements
f
(
ϵ
,
ℓ
;
r
)
=
(
-
1
)
ℓ
ν
ℓ
+
1
(
-
cos
(
π
ν
)
ζ
ℓ
(
ν
,
r
)
Γ
(
ℓ
+
1
+
ν
)
+
sin
(
π
ν
)
Γ
(
ν
-
ℓ
)
ξ
ℓ
(
ν
,
r
)
π
)
,
Coulomb-f
italic-ϵ
ℓ
𝑟
superscript
1
ℓ
superscript
𝜈
ℓ
1
𝜋
𝜈
subscript
𝜁
ℓ
𝜈
𝑟
Euler-Gamma
ℓ
1
𝜈
𝜋
𝜈
Euler-Gamma
𝜈
ℓ
subscript
𝜉
ℓ
𝜈
𝑟
𝜋
{\displaystyle{\displaystyle f\left(\epsilon,\ell;r\right)=(-1)^{\ell}\nu^{%
\ell+1}\left(-\frac{\cos\left(\pi\nu\right)\zeta_{\ell}(\nu,r)}{\Gamma\left(%
\ell+1+\nu\right)}+\frac{\sin\left(\pi\nu\right)\Gamma\left(\nu-\ell\right)\xi%
_{\ell}(\nu,r)}{\pi}\right),}}
f
(
ϵ
,
ℓ
;
r
)
Coulomb-f
italic-ϵ
ℓ
𝑟
{\displaystyle{\displaystyle f\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right%
)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
r
𝑟
{\displaystyle{\displaystyle r}}
ϵ
italic-ϵ
{\displaystyle{\displaystyle\epsilon}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
ζ
ℓ
(
ν
,
r
)
subscript
𝜁
ℓ
𝜈
𝑟
{\displaystyle{\displaystyle\zeta_{\ell}(\nu,r)}}
ξ
ℓ
(
ν
,
r
)
subscript
𝜉
ℓ
𝜈
𝑟
{\displaystyle{\displaystyle\xi_{\ell}(\nu,r)}}
Identifiers
