DLMF:26.4.E2 (Q7787)

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DLMF:26.4.E2
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    Statements

    Defining formula
    ( n 1 + n 2 + ⋯ + n k n 1 , n 2 , … , n k ) = ( n 1 + n 2 + ⋯ + n k ) ! n 1 ! ⁢ n 2 ! ⁢ ⋯ ⁢ n k ! = ∏ j = 1 k - 1 ( n j + n j + 1 + ⋯ + n k n j ) . multinomial subscript 𝑛 1 subscript 𝑛 2 ⋯ subscript 𝑛 𝑘 subscript 𝑛 1 subscript 𝑛 2 … subscript 𝑛 𝑘 subscript 𝑛 1 subscript 𝑛 2 ⋯ subscript 𝑛 𝑘 subscript 𝑛 1 subscript 𝑛 2 ⋯ subscript 𝑛 𝑘 superscript subscript product 𝑗 1 𝑘 1 binomial subscript 𝑛 𝑗 subscript 𝑛 𝑗 1 ⋯ subscript 𝑛 𝑘 subscript 𝑛 𝑗 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n_{1}+n_{2}+\cdots+n_{k}}{% n_{1},n_{2},\ldots,n_{k}}=\frac{(n_{1}+n_{2}+\cdots+n_{k})!}{n_{1}!\,n_{2}!\,% \cdots\,n_{k}!}=\prod_{j=1}^{k-1}\genfrac{(}{)}{0.0pt}{}{n_{j}+n_{j+1}+\cdots+% n_{k}}{n_{j}}.}}
    0 references
    DLMF id
    DLMF:26.4.E2
    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.m1aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q12175
    Defining formula
    ( n 1 + n 2 + … + n k n 1 , n 2 , … , n k ) multinomial subscript 𝑛 1 subscript 𝑛 2 … subscript 𝑛 𝑘 subscript 𝑛 1 subscript 𝑛 2 … subscript 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{n_{1}}+\NVar{n_{2}}+% \dots+\NVar{n_{k}}}{\NVar{n_{1}},\NVar{n_{2}},\ldots,\NVar{n_{k}}}}}
    xml-id
    C26.S4.SS1.p1.m2aadec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1dec
    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.m1adec
    0 references
     
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