DLMF:26.8.E25 (Q7853): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q12131 / rank
 
Normal rank
Property / Symbols used: Q12131 / qualifier
 
Defining formula:

S ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}

\StirlingnumberS@{\NVar{n}}{\NVar{k}}
Property / Symbols used: Q12131 / qualifier
 
xml-id: C26.S8.SS1.p3.m2amdec
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.m1addec
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.m1fdec
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.m1tdec
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.m1ydec

Latest revision as of 13:54, 2 January 2020

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DLMF:26.8.E25
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    Statements

    S ( n + 1 , k + 1 ) = j = k n ( n j ) S ( j , k ) , Stirling-number-second-kind-S 𝑛 1 𝑘 1 superscript subscript 𝑗 𝑘 𝑛 binomial 𝑛 𝑗 Stirling-number-second-kind-S 𝑗 𝑘 {\displaystyle{\displaystyle S\left(n+1,k+1\right)=\sum_{j=k}^{n}\genfrac{(}{)% }{0.0pt}{}{n}{j}S\left(j,k\right),}}
    0 references
    DLMF:26.8.E25
    0 references
    S ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}
    C26.S8.SS1.p3.m2amdec
    0 references
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1addec
    0 references
    j 𝑗 {\displaystyle{\displaystyle j}}
    C26.S1.XMD3.m1fdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C26.S1.XMD4.m1tdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C26.S1.XMD6.m1ydec
    0 references