DLMF:26.9.E4 (Q7877)

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DLMF:26.9.E4
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    Statements

    test
    [ m n ] q = ∏ j = 1 n 1 - q m - n + j 1 - q j , q-binomial 𝑚 𝑛 𝑞 superscript subscript product 𝑗 1 𝑛 1 superscript 𝑞 𝑚 𝑛 𝑗 1 superscript 𝑞 𝑗 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{m}{n}_{q}=\prod_{j=1}^{n}% \frac{1-q^{m-n+j}}{1-q^{j}},}}
    0 references
    DLMF id
    DLMF:26.9.E4
    0 references
    constraint
    n ≥ 0 𝑛 0 {\displaystyle{\displaystyle n\geq 0}}
    0 references
    Symbols used
    $$q$$ -binomial coefficient (or Gaussian polynomial)
    test
    [ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}
    xml-id
    C17.S2.E27.m2adec
    0 references
    Q12176
    test
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1dec
    0 references
     
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