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

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Property / 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}}

n_{1},n_{2},\ldots,n_{m}\geq 1
Property / 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}} / rank
 
Normal rank

Revision as of 18:20, 30 December 2019

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DLMF:26.4.E10
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    Statements

    ( 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}},}}
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    DLMF:26.4.E10
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    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