DLMF:17.2.E16 (Q5306)

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DLMF:17.2.E16
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    Statements

    Defining formula
    ( a ⁢ q - n ; q ) n - k = ( q / a ; q ) n ( q / a ; q ) k ⁢ ( - a q ) n - k ⁢ q ( k 2 ) - ( n 2 ) , q-Pochhammer-symbol 𝑎 superscript 𝑞 𝑛 𝑞 𝑛 𝑘 q-Pochhammer-symbol 𝑞 𝑎 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑎 𝑞 𝑘 superscript 𝑎 𝑞 𝑛 𝑘 superscript 𝑞 binomial 𝑘 2 binomial 𝑛 2 {\displaystyle{\displaystyle\left(aq^{-n};q\right)_{n-k}=\frac{\left(q/a;q% \right)_{n}}{\left(q/a;q\right)_{k}}\left(-\frac{a}{q}\right)^{n-k}q^{\genfrac% {(}{)}{0.0pt}{}{k}{2}-\genfrac{(}{)}{0.0pt}{}{n}{2}},}}
    0 references
    DLMF id
    DLMF:17.2.E16
    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.m1aedec
    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.m2aodec
    0 references
     
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