DLMF:26.8.E35 (Q7863): Difference between revisions

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‎Changed an Item: Add constraint
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.m1acdec

Revision as of 13:56, 2 January 2020

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DLMF:26.8.E35
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    Statements

    Defining formula
    ∑ j = 0 n j k = ∑ j = 0 k j ! ⁢ S ⁡ ( k , j ) ⁢ ( n + 1 j + 1 ) , superscript subscript 𝑗 0 𝑛 superscript 𝑗 𝑘 superscript subscript 𝑗 0 𝑘 𝑗 Stirling-number-second-kind-S 𝑘 𝑗 binomial 𝑛 1 𝑗 1 {\displaystyle{\displaystyle\sum_{j=0}^{n}j^{k}=\sum_{j=0}^{k}j!S\left(k,j% \right)\genfrac{(}{)}{0.0pt}{}{n+1}{j+1},}}
    0 references
    DLMF id
    DLMF:26.8.E35
    0 references
    Symbols used
    Q12131
    Defining formula
    S ⁡ ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p3.m2ardec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1agdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5ajdec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1ldec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1acdec
    0 references
     
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