DLMF:17.2.E29 (Q5319)

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DLMF:17.2.E29
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    Statements

    Defining formula
    [ m + n m ] q = ( q n + 1 ; q ) m ( q ; q ) m , q-binomial 𝑚 𝑛 𝑚 𝑞 q-Pochhammer-symbol superscript 𝑞 𝑛 1 𝑞 𝑚 q-Pochhammer-symbol 𝑞 𝑞 𝑚 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{m+n}{m}_{q}=\frac{\left(q^% {n+1};q\right)_{m}}{\left(q;q\right)_{m}},}}
    0 references
    DLMF id
    DLMF:17.2.E29
    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.m2aaadec
    0 references
    $$q$$ -binomial coefficient (or Gaussian polynomial)
    Defining formula
    [ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}
    xml-id
    C17.S2.E27.m2abdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1abdec
    0 references
    Q11716
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1bdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1ydec
    0 references
     
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