DLMF:33.6.E2 (Q9534)

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DLMF:33.6.E2
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    Statements

    Defining formula
    F ℓ ′ ⁡ ( η , ρ ) = C ℓ ⁡ ( η ) ⁢ ∑ k = ℓ + 1 ∞ k ⁢ A k ℓ ⁢ ( η ) ⁢ ρ k - 1 , diffop regular-Coulomb-F ℓ 1 𝜂 𝜌 Coulomb-C ℓ 𝜂 superscript subscript 𝑘 ℓ 1 𝑘 superscript subscript 𝐴 𝑘 ℓ 𝜂 superscript 𝜌 𝑘 1 {\displaystyle{\displaystyle F_{\ell}'\left(\eta,\rho\right)=C_{\ell}\left(% \eta\right)\sum_{k=\ell+1}^{\infty}kA_{k}^{\ell}(\eta)\rho^{k-1},}}
    0 references
    DLMF id
    DLMF:33.6.E2
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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.m2aadec
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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.m2aadec
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    Q12669
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C33.S1.XMD1.m1adec
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    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1adec
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    Q12667
    Defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C33.S1.XMD5.m1adec
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    Q12668
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C33.S1.XMD7.m1adec
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    Q12675
    Defining formula
    A ℓ + 1 ℓ superscript subscript 𝐴 ℓ 1 ℓ {\displaystyle{\displaystyle A_{\ell+1}^{\ell}}}
    xml-id
    C33.S6.XMD1.m1adec
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