DLMF:26.14.E6 (Q7957): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
Defining formula:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1aadec
Property / Symbols used
 
Property / Symbols used: Q12176 / rank
 
Normal rank
Property / Symbols used: Q12176 / qualifier
 
Defining formula:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q12176 / qualifier
 
xml-id: C26.S1.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12174 / rank
 
Normal rank
Property / Symbols used: Q12174 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12174 / qualifier
 
xml-id: C26.S1.XMD4.m1ddec
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.m1fdec

Latest revision as of 14:08, 2 January 2020

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DLMF:26.14.E6
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    Statements

    n k = j = 0 k ( - 1 ) j ( n + 1 j ) ( k + 1 - j ) n , Eulerian-number 𝑛 𝑘 superscript subscript 𝑗 0 𝑘 superscript 1 𝑗 binomial 𝑛 1 𝑗 superscript 𝑘 1 𝑗 𝑛 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{n}{k}=\sum_{j=0}^{k}(-1)^{% j}\genfrac{(}{)}{0.0pt}{}{n+1}{j}(k+1-j)^{n},}}
    0 references
    DLMF:26.14.E6
    0 references
    n 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}
    0 references
    n k Eulerian-number 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}}
    C26.S14.SS1.p3.m2acdec
    0 references
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1aadec
    0 references
    j 𝑗 {\displaystyle{\displaystyle j}}
    C26.S1.XMD3.m1cdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C26.S1.XMD4.m1ddec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C26.S1.XMD6.m1fdec
    0 references