DLMF:5.18.E6 (Q2193)

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DLMF:5.18.E6
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    Statements

    Defining formula
    n ⁢ \lxMathTweak ⁢ r ⁢ o ⁢ l ⁢ e = P ⁢ O ⁢ S ⁢ T ⁢ F ⁢ I ⁢ X ! q = Γ q ⁡ ( n + 1 ) , q-factorial 𝑛 𝑞 q-Gamma 𝑞 𝑛 1 {\displaystyle{\displaystyle n\lxMathTweak{role=POSTFIX}{\@nonfactorial_{q}}=% \Gamma_{q}\left(n+1\right),}}
    0 references
    DLMF id
    DLMF:5.18.E6
    0 references
    Symbols used
    $$q$$ -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.m2abdec
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    $$q$$ -factorial (as in $$n!_{q}$$ )
    Defining formula
    \lxMathTweak ⁢ r ⁢ o ⁢ l ⁢ e = P ⁢ O ⁢ S ⁢ T ⁢ F ⁢ I ⁢ X ! q q-factorial 𝑞 {\displaystyle{\displaystyle\lxMathTweak{role=POSTFIX}{\@nonfactorial_{\NVar{q% }}}}}
    xml-id
    C5.S18.E2.m2aadec
    0 references
    Q11280
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C5.S1.XMD10.m1edec
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    Q11274
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1bdec
    0 references
     
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