DLMF:33.2.E6 (Q10193)

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DLMF:33.2.E6
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    Statements

    DLMF defining formula
    C ℓ ⁡ ( η ) = 2 ℓ ⁢ ( ( 2 ⁢ π ⁢ η / ( e 2 ⁢ π ⁢ η - 1 ) ) ⁢ ∏ k = 1 ℓ ( η 2 + k 2 ) ) 1 / 2 ( 2 ⁢ ℓ + 1 ) ! . Coulomb-C ℓ 𝜂 superscript 2 ℓ superscript 2 𝜋 𝜂 superscript 𝑒 2 𝜋 𝜂 1 superscript subscript product 𝑘 1 ℓ superscript 𝜂 2 superscript 𝑘 2 1 2 2 ℓ 1 {\displaystyle{\displaystyle C_{\ell}\left(\eta\right)=\dfrac{2^{\ell}\left((2% \pi\eta/(e^{2\pi\eta}-1))\prod_{k=1}^{\ell}(\eta^{2}+k^{2})\right)^{\ifrac{1}{% 2}}}{(2\ell+1)!}.}}
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    Symbols used
    normalizing constant for Coulomb radial functions
    DLMF defining formula
    C ℓ ⁡ ( η ) Coulomb-C ℓ 𝜂 {\displaystyle{\displaystyle C_{\NVar{\ell}}\left(\NVar{\eta}\right)}}
    xml-id
    C33.S2.E5.m2acdec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C33.S1.XMD1.m1dec
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    nonnegative integer
    DLMF defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1edec
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    real parameter
    DLMF defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C33.S1.XMD7.m1edec
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    Identifiers

     
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