DLMF:5.18.E4 (Q2191)

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DLMF:5.18.E4
No description defined

    Statements

    Defining formula
    Γ q ⁡ ( z ) = ( q ; q ) ∞ ⁢ ( 1 - q ) 1 - z / ( q z ; q ) ∞ , q-Gamma 𝑞 𝑧 q-Pochhammer-symbol 𝑞 𝑞 superscript 1 𝑞 1 𝑧 q-Pochhammer-symbol superscript 𝑞 𝑧 𝑞 {\displaystyle{\displaystyle\Gamma_{q}\left(z\right)=\left(q;q\right)_{\infty}% (1-q)^{1-z}/\left(q^{z};q\right)_{\infty},}}
    0 references
    DLMF id
    DLMF:5.18.E4
    0 references
    Symbols used
    Q11298
    Defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2acdec
    0 references
    Q11280
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C5.S1.XMD10.m1cdec
    0 references
    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1dec
    0 references
     
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