DLMF:26.4.E10 (Q7795): Difference between revisions

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‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1jdec

Latest revision as of 01:10, 2 January 2020

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DLMF:26.4.E10
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    Statements

    Defining formula
    ( n 1 + n 2 + ⋯ + n m n 1 , n 2 , … , n m ) = ∑ k = 1 m ( n 1 + n 2 + ⋯ + n m - 1 n 1 , n 2 , … , n k - 1 , n k - 1 , n k + 1 , … , n m ) , multinomial subscript 𝑛 1 subscript 𝑛 2 ⋯ subscript 𝑛 𝑚 subscript 𝑛 1 subscript 𝑛 2 … subscript 𝑛 𝑚 superscript subscript 𝑘 1 𝑚 multinomial subscript 𝑛 1 subscript 𝑛 2 ⋯ subscript 𝑛 𝑚 1 subscript 𝑛 1 subscript 𝑛 2 … subscript 𝑛 𝑘 1 subscript 𝑛 𝑘 1 subscript 𝑛 𝑘 1 … subscript 𝑛 𝑚 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n_{1}+n_{2}+\cdots+n_{m}}{% n_{1},n_{2},\ldots,n_{m}}=\sum_{k=1}^{m}\genfrac{(}{)}{0.0pt}{}{n_{1}+n_{2}+% \cdots+n_{m}-1}{n_{1},n_{2},\ldots,n_{k-1},n_{k}-1,n_{k+1},\ldots,n_{m}},}}
    0 references
    DLMF id
    DLMF:26.4.E10
    0 references
    constraint
    n 1 , n 2 , … , n m ≥ 1 subscript 𝑛 1 subscript 𝑛 2 … subscript 𝑛 𝑚 1 {\displaystyle{\displaystyle n_{1},n_{2},\ldots,n_{m}\geq 1}}
    0 references
    Symbols used
    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.m2acdec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1bdec
    0 references
    Q12171
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C26.S1.XMD5.m1bdec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1jdec
    0 references
     
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