DLMF:33.2.E13 (Q9509)

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DLMF:33.2.E13
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    Statements

    Defining formula
    F ℓ - 1 ⁢ G ℓ - F ℓ ⁢ G ℓ - 1 = ℓ / ( ℓ 2 + η 2 ) 1 / 2 , regular-Coulomb-F ℓ 1 irregular-Coulomb-G ℓ regular-Coulomb-F ℓ irregular-Coulomb-G ℓ 1 ℓ superscript superscript ℓ 2 superscript 𝜂 2 1 2 {\displaystyle{\displaystyle F_{\ell-1}G_{\ell}-F_{\ell}G_{\ell-1}=\ell/(\ell^% {2}+\eta^{2})^{1/2},}}
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    DLMF id
    DLMF:33.2.E13
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    constraint
    ℓ ≥ 1 ℓ 1 {\displaystyle{\displaystyle\ell\geq 1}}
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    Symbols used
    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.m1abdec
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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.m2addec
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    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1ldec
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    Q12668
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C33.S1.XMD7.m1kdec
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