DLMF:5.18.E2 (Q2189)

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DLMF:5.18.E2
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    Statements

    Defining formula
    n ⁢ \lxMathTweak ⁢ r ⁢ o ⁢ l ⁢ e = P ⁢ O ⁢ S ⁢ T ⁢ F ⁢ I ⁢ X ! q = 1 ⁢ ( 1 + q ) ⁢ ⋯ ⁢ ( 1 + q + … + q n - 1 ) = ( q ; q ) n ⁢ ( 1 - q ) - n . q-factorial 𝑛 𝑞 1 1 𝑞 ⋯ 1 𝑞 … superscript 𝑞 𝑛 1 q-Pochhammer-symbol 𝑞 𝑞 𝑛 superscript 1 𝑞 𝑛 {\displaystyle{\displaystyle n\lxMathTweak{role=POSTFIX}{\@nonfactorial_{q}}=1% (1+q)\cdots(1+q+\dots+q^{n-1})=\left(q;q\right)_{n}(1-q)^{-n}.}}
    0 references
    DLMF id
    DLMF:5.18.E2
    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.m2aadec
    0 references
    Q11280
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C5.S1.XMD10.m1adec
    0 references
     
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