DLMF:17.2.E28 (Q5318)

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DLMF:17.2.E28
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    Statements

    Defining formula
    lim q → 1 ⁡ [ n m ] q = ( n m ) = n ! m ! ⁢ ( n - m ) ! , subscript → 𝑞 1 q-binomial 𝑛 𝑚 𝑞 binomial 𝑛 𝑚 𝑛 𝑚 𝑛 𝑚 {\displaystyle{\displaystyle\lim_{q\to 1}\genfrac{[}{]}{0.0pt}{}{n}{m}_{q}=% \genfrac{(}{)}{0.0pt}{}{n}{m}=\frac{n!}{m!(n-m)!},}}
    0 references
    DLMF id
    DLMF:17.2.E28
    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.m1aidec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    $$q$$ -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.m2aadec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1aadec
    0 references
    Q11716
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1adec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1xdec
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