DLMF:17.2.E32 (Q5322)

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DLMF:17.2.E32
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    Statements

    Defining formula
    [ n m ] q = [ n - 1 m ] q + q n - m ⁢ [ n - 1 m - 1 ] q , q-binomial 𝑛 𝑚 𝑞 q-binomial 𝑛 1 𝑚 𝑞 superscript 𝑞 𝑛 𝑚 q-binomial 𝑛 1 𝑚 1 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{n}{m}_{q}=\genfrac{[}{]}{0% .0pt}{}{n-1}{m}_{q}+q^{n-m}\genfrac{[}{]}{0.0pt}{}{n-1}{m-1}_{q},}}
    0 references
    DLMF id
    DLMF:17.2.E32
    0 references
    Symbols used
    $$q$$ -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.m2aedec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1aedec
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    Q11716
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1edec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1abdec
    0 references
     
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