DLMF:33.2.E5 (Q9500)

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DLMF:33.2.E5
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    Statements

    Defining formula
    C ℓ ⁡ ( η ) = 2 ℓ ⁢ e - π ⁢ η / 2 ⁢ | Γ ⁡ ( ℓ + 1 + i ⁢ η ) | ( 2 ⁢ ℓ + 1 ) ! . Coulomb-C ℓ 𝜂 superscript 2 ℓ superscript 𝑒 𝜋 𝜂 2 Euler-Gamma ℓ 1 imaginary-unit 𝜂 2 ℓ 1 {\displaystyle{\displaystyle C_{\ell}\left(\eta\right)=\frac{2^{\ell}e^{-\pi% \eta/2}|\Gamma\left(\ell+1+\mathrm{i}\eta\right)|}{(2\ell+1)!}.}}
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    DLMF id
    DLMF:33.2.E5
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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