DLMF:26.8.E20 (Q7848): Difference between revisions

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‎Changed an Item: Add constraint
‎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.m1tdec

Latest revision as of 13:54, 2 January 2020

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DLMF:26.8.E20
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    Statements

    Defining formula
    s ⁡ ( n + 1 , k + 1 ) = n ! ⁢ ∑ j = k n ( - 1 ) n - j j ! ⁢ s ⁡ ( j , k ) , Stirling-number-first-kind-S 𝑛 1 𝑘 1 𝑛 superscript subscript 𝑗 𝑘 𝑛 superscript 1 𝑛 𝑗 𝑗 Stirling-number-first-kind-S 𝑗 𝑘 {\displaystyle{\displaystyle s\left(n+1,k+1\right)=n!\sum_{j=k}^{n}\frac{(-1)^% {n-j}}{j!}\,s\left(j,k\right),}}
    0 references
    DLMF id
    DLMF:26.8.E20
    0 references
    Symbols used
    Q12132
    Defining formula
    s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p1.m5aldec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5agdec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1bdec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1odec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1tdec
    0 references
     
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