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Statements
H
ℓ
±
(
η
,
ρ
)
=
(
∓
i
)
ℓ
e
(
π
η
/
2
)
±
i
σ
ℓ
(
η
)
W
∓
i
η
,
ℓ
+
1
2
(
∓
2
i
ρ
)
,
irregular-Coulomb-H
plus-or-minus
ℓ
𝜂
𝜌
superscript
minus-or-plus
imaginary-unit
ℓ
superscript
𝑒
plus-or-minus
𝜋
𝜂
2
imaginary-unit
Coulomb-phase-shift
ℓ
𝜂
Whittaker-confluent-hypergeometric-W
minus-or-plus
imaginary-unit
𝜂
ℓ
1
2
minus-or-plus
2
imaginary-unit
𝜌
{\displaystyle{\displaystyle{H^{\pm}_{\ell}}\left(\eta,\rho\right)=(\mp\mathrm%
{i})^{\ell}e^{(\pi\eta/2)\pm\mathrm{i}{\sigma_{\ell}}\left(\eta\right)}W_{\mp%
\mathrm{i}\eta,\ell+\frac{1}{2}}\left(\mp 2\mathrm{i}\rho\right),}}
σ
ℓ
(
η
)
Coulomb-phase-shift
ℓ
𝜂
{\displaystyle{\displaystyle{\sigma_{\NVar{\ell}}}\left(\NVar{\eta}\right)}}
W
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-W
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
η
𝜂
{\displaystyle{\displaystyle\eta}}
Identifiers
