DLMF:5.18.E10 (Q2197)

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DLMF:5.18.E10
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    Statements

    Defining formula
    lim q → 1 - ⁡ Γ q ⁡ ( z ) = Γ ⁡ ( z ) . subscript → 𝑞 limit-from 1 q-Gamma 𝑞 𝑧 Euler-Gamma 𝑧 {\displaystyle{\displaystyle\lim_{q\to 1-}\Gamma_{q}\left(z\right)=\Gamma\left% (z\right).}}
    0 references
    DLMF id
    DLMF:5.18.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.m2adec
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    $$q$$ -gamma function
    Defining formula
    Γ q ⁡ ( z ) q-Gamma 𝑞 𝑧 {\displaystyle{\displaystyle\Gamma_{\NVar{q}}\left(\NVar{z}\right)}}
    xml-id
    C5.S18.E4.m2afdec
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    Q11280
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C5.S1.XMD10.m1idec
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    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1bdec
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