DLMF:26.14.E8 (Q7959): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12217 / rank
 
Normal rank
Property / Symbols used: Q12217 / qualifier
 
test:

⟨ n k ⟩ Eulerian-number 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}}

\Euleriannumber{\NVar{n}}{\NVar{k}}
Property / Symbols used: Q12217 / qualifier
 
xml-id: C26.S14.SS1.p3.m2aedec
Property / Symbols used
 
Property / Symbols used: Q12174 / rank
 
Normal rank
Property / Symbols used: Q12174 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

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

Latest revision as of 13:08, 2 January 2020

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DLMF:26.14.E8
No description defined

    Statements

    test
    ⟨ n k ⟩ = ( k + 1 ) ⁢ ⟨ n - 1 k ⟩ + ( n - k ) ⁢ ⟨ n - 1 k - 1 ⟩ , Eulerian-number 𝑛 𝑘 𝑘 1 Eulerian-number 𝑛 1 𝑘 𝑛 𝑘 Eulerian-number 𝑛 1 𝑘 1 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{n}{k}=(k+1)\genfrac{<}{>}{% 0.0pt}{}{n-1}{k}+(n-k)\genfrac{<}{>}{0.0pt}{}{n-1}{k-1},}}
    0 references
    DLMF id
    DLMF:26.14.E8
    0 references
    constraint
    n ≥ 2 𝑛 2 {\displaystyle{\displaystyle n\geq 2}}
    0 references
    Symbols used
    Q12217
    test
    ⟨ n k ⟩ Eulerian-number 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}}
    xml-id
    C26.S14.SS1.p3.m2aedec
    0 references
    Q12174
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1fdec
    0 references
     
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