DLMF:26.8.E23 (Q7851): Difference between revisions

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Property / constraint
 

n ≥ k ≥ h 𝑛 𝑘 ℎ {\displaystyle{\displaystyle n\geq k\geq h}}

n\geq k\geq h
Property / constraint: n ≥ k ≥ h 𝑛 𝑘 ℎ {\displaystyle{\displaystyle n\geq k\geq h}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q12131 / rank
 
Normal rank
Property / Symbols used: Q12131 / qualifier
 
test:

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.m2akdec
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
test:

( 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.m1acdec
Property / Symbols used
 
Property / Symbols used: Q12186 / rank
 
Normal rank
Property / Symbols used: Q12186 / qualifier
 
test:

h ℎ {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q12186 / qualifier
 
xml-id: C26.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q12176 / rank
 
Normal rank
Property / Symbols used: Q12176 / qualifier
 
test:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q12176 / qualifier
 
xml-id: C26.S1.XMD3.m1ddec
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.m1rdec
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1wdec

Latest revision as of 12:54, 2 January 2020

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DLMF:26.8.E23
No description defined

    Statements

    test
    ( k h ) ⁢ S ⁡ ( n , k ) = ∑ j = k - h n - h ( n j ) ⁢ S ⁡ ( n - j , h ) ⁢ S ⁡ ( j , k - h ) , binomial 𝑘 ℎ Stirling-number-second-kind-S 𝑛 𝑘 superscript subscript 𝑗 𝑘 ℎ 𝑛 ℎ binomial 𝑛 𝑗 Stirling-number-second-kind-S 𝑛 𝑗 ℎ Stirling-number-second-kind-S 𝑗 𝑘 ℎ {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{k}{h}S\left(n,k\right)=% \sum_{j=k-h}^{n-h}\genfrac{(}{)}{0.0pt}{}{n}{j}S\left(n-j,h\right)S\left(j,k-h% \right),}}
    0 references
    DLMF id
    DLMF:26.8.E23
    0 references
    constraint
    n ≥ k ≥ h 𝑛 𝑘 ℎ {\displaystyle{\displaystyle n\geq k\geq h}}
    0 references
    Symbols used
    Q12131
    test
    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.m2akdec
    0 references
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1acdec
    0 references
    Q12186
    test
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C26.S1.XMD2.m1adec
    0 references
    Q12176
    test
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1ddec
    0 references
    Q12174
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1rdec
    0 references
    Q12172
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1wdec
    0 references
     
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