DLMF:33.2.E12 (Q9508)

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DLMF:33.2.E12
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    Statements

    Defining formula
    𝒲 ⁡ { G ℓ , F ℓ } = 𝒲 ⁡ { H ℓ ± , F ℓ } = 1 . Wronskian irregular-Coulomb-G ℓ regular-Coulomb-F ℓ Wronskian irregular-Coulomb-H plus-or-minus ℓ regular-Coulomb-F ℓ 1 {\displaystyle{\displaystyle\mathscr{W}\left\{G_{\ell},F_{\ell}\right\}=% \mathscr{W}\left\{{H^{\pm}_{\ell}},F_{\ell}\right\}=1.}}
    0 references
    DLMF id
    DLMF:33.2.E12
    0 references
    Symbols used
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3adec
    0 references
    Q12670
    Defining formula
    G ℓ ⁡ ( η , ρ ) irregular-Coulomb-G ℓ 𝜂 𝜌 {\displaystyle{\displaystyle G_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}% \right)}}
    xml-id
    C33.S2.E11.m1aadec
    0 references
    irregular Coulomb radial functions
    Defining formula
    H ℓ ± ⁡ ( η , ρ ) irregular-Coulomb-H plus-or-minus ℓ 𝜂 𝜌 {\displaystyle{\displaystyle{H^{\NVar{\pm}}_{\NVar{\ell}}}\left(\NVar{\eta},% \NVar{\rho}\right)}}
    xml-id
    C33.S2.E7.m2acdec
    0 references
    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.m2acdec
    0 references
    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1kdec
    0 references
     
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