DLMF:26.16.E1 (Q7981)

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DLMF:26.16.E1
No description defined

    Statements

    Defining formula
    [ a 1 + a 2 + ⋯ + a n a 1 , a 2 , … , a n ] q = ∏ k = 1 n - 1 [ a k + a k + 1 + ⋯ + a n a k ] q , q-multinomial subscript 𝑎 1 subscript 𝑎 2 ⋯ subscript 𝑎 𝑛 subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑛 𝑞 superscript subscript product 𝑘 1 𝑛 1 q-binomial subscript 𝑎 𝑘 subscript 𝑎 𝑘 1 ⋯ subscript 𝑎 𝑛 subscript 𝑎 𝑘 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{a_{1}+a_{2}+\cdots+a_{n}}{% a_{1},a_{2},\ldots,a_{n}}_{q}=\prod_{k=1}^{n-1}\genfrac{[}{]}{0.0pt}{}{a_{k}+a% _{k+1}+\cdots+a_{n}}{a_{k}}_{q},}}
    0 references
    DLMF id
    DLMF:26.16.E1
    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.m2adec
    0 references
    Q12224
    Defining formula
    [ a 1 + a 2 + … + a n a 1 , a 2 , … , a n ] q q-multinomial subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑛 subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑛 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{a_{1}}+\NVar{a_{2}}+% \dots+\NVar{a_{n}}}{\NVar{a_{1}},\NVar{a_{2}},\ldots,\NVar{a_{n}}}_{\NVar{q}}}}
    xml-id
    C26.S16.p3.m2adec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1dec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1dec
    0 references
    Q12225
    Defining formula
    a j subscript 𝑎 𝑗 {\displaystyle{\displaystyle a_{j}}}
    xml-id
    C26.S16.XMD1.m1dec
    0 references
    Q12189
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C26.S9.XMD1.m1dec
    0 references
     
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