DLMF:26.14.E10 (Q7961): Difference between revisions

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Changed an Item: Add constraint
 
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Property / constraint
 

n 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}

n\geq 1
Property / constraint: n 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q12217 / rank
 
Normal rank
Property / Symbols used: Q12217 / qualifier
 
Defining formula:

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.m2agdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec
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.m1hdec
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 14:09, 2 January 2020

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DLMF:26.14.E10
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    Statements

    k = 0 n - 1 n k = n ! , superscript subscript 𝑘 0 𝑛 1 Eulerian-number 𝑛 𝑘 𝑛 {\displaystyle{\displaystyle\sum_{k=0}^{n-1}\genfrac{<}{>}{0.0pt}{}{n}{k}=n!,}}
    0 references
    DLMF:26.14.E10
    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.m2agdec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C26.S1.XMD4.m1hdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C26.S1.XMD6.m1jdec
    0 references