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DLMF:17.2.E31 - MaRDI portal

DLMF:17.2.E31 (Q6018)

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DLMF:17.2.E31
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    Statements

    DLMF defining formula
    [ n m ] q = [ n - 1 m - 1 ] q + q m ⁢ [ n - 1 m ] q , q-binomial 𝑛 𝑚 𝑞 q-binomial 𝑛 1 𝑚 1 𝑞 superscript 𝑞 𝑚 q-binomial 𝑛 1 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{n}{m}_{q}=\genfrac{[}{]}{0% .0pt}{}{n-1}{m-1}_{q}+q^{m}\genfrac{[}{]}{0.0pt}{}{n-1}{m}_{q},}}
    0 references
    Symbols used
    $$q$$ -binomial coefficient (or Gaussian polynomial)
    DLMF 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.m2addec
    0 references
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1addec
    0 references
    nonnegative integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1ddec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1aadec
    0 references
     
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