DLMF:33.16.E1 (Q9628)

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DLMF:33.16.E1
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    Statements

    Defining formula
    F ℓ ⁡ ( η , ρ ) = ( 2 ⁢ ℓ + 1 ) ! ⁢ C ℓ ⁡ ( η ) ( - 2 ⁢ η ) ℓ + 1 ⁢ f ⁡ ( 1 / η 2 , ℓ ; - η ⁢ ρ ) , regular-Coulomb-F ℓ 𝜂 𝜌 2 ℓ 1 Coulomb-C ℓ 𝜂 superscript 2 𝜂 ℓ 1 Coulomb-f 1 superscript 𝜂 2 ℓ 𝜂 𝜌 {\displaystyle{\displaystyle F_{\ell}\left(\eta,\rho\right)=\dfrac{(2\ell+1)!C% _{\ell}\left(\eta\right)}{(-2\eta)^{\ell+1}}f\left(1/\eta^{2},\ell;-\eta\rho% \right),}}
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    DLMF id
    DLMF:33.16.E1
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    Symbols used
    normalizing constant for Coulomb radial functions
    Defining formula
    C ℓ ⁡ ( η ) Coulomb-C ℓ 𝜂 {\displaystyle{\displaystyle C_{\NVar{\ell}}\left(\NVar{\eta}\right)}}
    xml-id
    C33.S2.E5.m2adec
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    regular Coulomb function
    Defining formula
    f ⁡ ( ϵ , ℓ ; r ) Coulomb-f italic-ϵ ℓ 𝑟 {\displaystyle{\displaystyle f\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right% )}}
    xml-id
    C33.S14.E4.m2adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    regular Coulomb radial function
    Defining formula
    F ℓ ⁡ ( η , ρ ) regular-Coulomb-F ℓ 𝜂 𝜌 {\displaystyle{\displaystyle F_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}% \right)}}
    xml-id
    C33.S2.E3.m2adec
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    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1dec
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    Q12667
    Defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C33.S1.XMD5.m1dec
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    Q12668
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C33.S1.XMD7.m1dec
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