DLMF:33.2.E10 (Q9505)

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DLMF:33.2.E10
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    Statements

    Defining formula
    σ ℓ ⁡ ( η ) = ph ⁡ Γ ⁡ ( ℓ + 1 + i ⁢ η ) , Coulomb-phase-shift ℓ 𝜂 phase Euler-Gamma ℓ 1 imaginary-unit 𝜂 {\displaystyle{\displaystyle{\sigma_{\ell}}\left(\eta\right)=\operatorname{ph}% \Gamma\left(\ell+1+\mathrm{i}\eta\right),}}
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    DLMF id
    DLMF:33.2.E10
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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.m2aadec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
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    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1idec
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    Q12668
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C33.S1.XMD7.m1idec
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