DLMF:17.2.E27 (Q5317)

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DLMF:17.2.E27
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    test
    [ n m ] q = ( q ; q ) n ( q ; q ) m ⁢ ( q ; q ) n - m = ( q - n ; q ) m ⁢ ( - 1 ) m ⁢ q n ⁢ m - ( m 2 ) ( q ; q ) m , q-binomial 𝑛 𝑚 𝑞 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑚 q-Pochhammer-symbol 𝑞 𝑞 𝑛 𝑚 q-Pochhammer-symbol superscript 𝑞 𝑛 𝑞 𝑚 superscript 1 𝑚 superscript 𝑞 𝑛 𝑚 binomial 𝑚 2 q-Pochhammer-symbol 𝑞 𝑞 𝑚 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{n}{m}_{q}=\frac{\left(q;q% \right)_{n}}{\left(q;q\right)_{m}\left(q;q\right)_{n-m}}\\ =\frac{\left(q^{-n};q\right)_{m}(-1)^{m}q^{nm-\genfrac{(}{)}{0.0pt}{}{m}{2}}}{% \left(q;q\right)_{m}},}}
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    DLMF id
    DLMF:17.2.E27
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