DLMF:33.17.E3 (Q9653)

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DLMF:33.17.E3
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    Statements

    Defining formula
    ( ℓ + 1 ) ⁢ r ⁢ f ′ ⁡ ( ϵ , ℓ ; r ) = ( ( ℓ + 1 ) 2 - r ) ⁢ f ⁡ ( ϵ , ℓ ; r ) - ( 1 + ( ℓ + 1 ) 2 ⁢ ϵ ) ⁢ r ⁢ f ⁡ ( ϵ , ℓ + 1 ; r ) , ℓ 1 𝑟 diffop Coulomb-f 1 italic-ϵ ℓ 𝑟 superscript ℓ 1 2 𝑟 Coulomb-f italic-ϵ ℓ 𝑟 1 superscript ℓ 1 2 italic-ϵ 𝑟 Coulomb-f italic-ϵ ℓ 1 𝑟 {\displaystyle{\displaystyle(\ell+1)rf'\left(\epsilon,\ell;r\right)=\left((% \ell+1)^{2}-r\right)f\left(\epsilon,\ell;r\right)-\left(1+(\ell+1)^{2}\epsilon% \right)rf\left(\epsilon,\ell+1;r\right),}}
    0 references
    DLMF id
    DLMF:33.17.E3
    0 references
    Symbols used
    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.m2aadec
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    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1bdec
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    Q12692
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C33.S1.XMD3.m1bdec
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    Q12693
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C33.S1.XMD6.m1bdec
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