DLMF:33.2.E8 (Q9503)

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DLMF:33.2.E8
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    H ± ( η , ρ ) = e ± i θ ( η , ρ ) ( 2 i ρ ) + 1 ± i η U ( + 1 ± i η , 2 + 2 , 2 i ρ ) , irregular-Coulomb-H plus-or-minus 𝜂 𝜌 superscript 𝑒 plus-or-minus imaginary-unit Coulomb-phase 𝜂 𝜌 superscript minus-or-plus 2 imaginary-unit 𝜌 plus-or-minus 1 imaginary-unit 𝜂 Kummer-confluent-hypergeometric-U plus-or-minus 1 imaginary-unit 𝜂 2 2 minus-or-plus 2 imaginary-unit 𝜌 {\displaystyle{\displaystyle{H^{\pm}_{\ell}}\left(\eta,\rho\right)=e^{\pm% \mathrm{i}{\theta_{\ell}}\left(\eta,\rho\right)}(\mp 2\mathrm{i}\rho)^{\ell+1% \pm\mathrm{i}\eta}U\left(\ell+1\pm\mathrm{i}\eta,2\ell+2,\mp 2\mathrm{i}\rho% \right),}}
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    DLMF:33.2.E8
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    θ ( η , ρ ) Coulomb-phase 𝜂 𝜌 {\displaystyle{\displaystyle{\theta_{\NVar{\ell}}}\left(\NVar{\eta},\NVar{\rho% }\right)}}
    C33.S2.E9.m2adec
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