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Statements
F
ℓ
(
η
,
ρ
)
=
ρ
ℓ
+
1
2
ℓ
e
i
ρ
-
(
π
η
/
2
)
|
Γ
(
ℓ
+
1
+
i
η
)
|
∫
0
1
e
-
2
i
ρ
t
t
ℓ
+
i
η
(
1
-
t
)
ℓ
-
i
η
d
t
,
regular-Coulomb-F
ℓ
𝜂
𝜌
superscript
𝜌
ℓ
1
superscript
2
ℓ
superscript
𝑒
imaginary-unit
𝜌
𝜋
𝜂
2
Euler-Gamma
ℓ
1
imaginary-unit
𝜂
superscript
subscript
0
1
superscript
𝑒
2
imaginary-unit
𝜌
𝑡
superscript
𝑡
ℓ
imaginary-unit
𝜂
superscript
1
𝑡
ℓ
imaginary-unit
𝜂
𝑡
{\displaystyle{\displaystyle F_{\ell}\left(\eta,\rho\right)=\frac{\rho^{\ell+1%
}2^{\ell}e^{\mathrm{i}\rho-(\pi\eta/2)}}{|\Gamma\left(\ell+1+\mathrm{i}\eta%
\right)|}\int_{0}^{1}e^{-2\mathrm{i}\rho t}t^{\ell+\mathrm{i}\eta}(1-t)^{\ell-%
\mathrm{i}\eta}\mathrm{d}t,}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
F
ℓ
(
η
,
ρ
)
regular-Coulomb-F
ℓ
𝜂
𝜌
{\displaystyle{\displaystyle F_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}%
\right)}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
η
𝜂
{\displaystyle{\displaystyle\eta}}
Identifiers
