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DLMF:33.17.E1 - MaRDI portal

DLMF:33.17.E1 (Q10343)

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DLMF:33.17.E1
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    Statements

    DLMF defining formula
    ( ℓ + 1 ) ⁢ r ⁢ f ⁡ ( ϵ , ℓ - 1 ; r ) - ( 2 ⁢ ℓ + 1 ) ⁢ ( ℓ ⁢ ( ℓ + 1 ) - r ) ⁢ f ⁡ ( ϵ , ℓ ; r ) + ℓ ⁢ ( 1 + ( ℓ + 1 ) 2 ⁢ ϵ ) ⁢ r ⁢ f ⁡ ( ϵ , ℓ + 1 ; r ) = 0 , ℓ 1 𝑟 Coulomb-f italic-ϵ ℓ 1 𝑟 2 ℓ 1 ℓ ℓ 1 𝑟 Coulomb-f italic-ϵ ℓ 𝑟 ℓ 1 superscript ℓ 1 2 italic-ϵ 𝑟 Coulomb-f italic-ϵ ℓ 1 𝑟 0 {\displaystyle{\displaystyle(\ell+1)rf\left(\epsilon,\ell-1;r\right)-(2\ell+1)% \left(\ell(\ell+1)-r\right)f\left(\epsilon,\ell;r\right)+\ell\left(1+(\ell+1)^% {2}\epsilon\right)rf\left(\epsilon,\ell+1;r\right)=0,}}
    0 references
    Symbols used
    regular Coulomb function
    DLMF 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
    0 references
    nonnegative integer
    DLMF defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1dec
    0 references
    real variable
    DLMF defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C33.S1.XMD3.m1dec
    0 references
    real parameter
    DLMF defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C33.S1.XMD6.m1dec
    0 references

    Identifiers

     
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