DLMF:17.2.E30 (Q5320)

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DLMF:17.2.E30
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    Statements

    Defining formula
    [ - n m ] q = [ m + n - 1 m ] q ⁢ ( - 1 ) m ⁢ q - m ⁢ n - ( m 2 ) , q-binomial 𝑛 𝑚 𝑞 q-binomial 𝑚 𝑛 1 𝑚 𝑞 superscript 1 𝑚 superscript 𝑞 𝑚 𝑛 binomial 𝑚 2 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{-n}{m}_{q}=\genfrac{[}{]}{% 0.0pt}{}{m+n-1}{m}_{q}(-1)^{m}q^{-mn-\genfrac{(}{)}{0.0pt}{}{m}{2}},}}
    0 references
    DLMF id
    DLMF:17.2.E30
    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.m1ajdec
    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.m2acdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1acdec
    0 references
    Q11716
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1cdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1zdec
    0 references
     
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