DLMF:17.2.E2 (Q5292)

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DLMF:17.2.E2
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    Statements

    Defining formula
    ( a ; q ) - n = 1 ( a ⁢ q - n ; q ) n = ( - q / a ) n ⁢ q ( n 2 ) ( q / a ; q ) n . q-Pochhammer-symbol 𝑎 𝑞 𝑛 1 q-Pochhammer-symbol 𝑎 superscript 𝑞 𝑛 𝑞 𝑛 superscript 𝑞 𝑎 𝑛 superscript 𝑞 binomial 𝑛 2 q-Pochhammer-symbol 𝑞 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(a;q\right)_{-n}=\frac{1}{\left(aq^{-n};q% \right)_{n}}=\frac{(-q/a)^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}}{\left(q/a;q% \right)_{n}}.}}
    0 references
    DLMF id
    DLMF:17.2.E2
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    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
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1adec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1adec
    0 references
     
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