DLMF:26.7.E2 (Q7818): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12184 / rank
 
Normal rank
Property / Symbols used: Q12184 / qualifier
 
Defining formula:

B ( n ) Bell-number 𝑛 {\displaystyle{\displaystyle B\left(\NVar{n}\right)}}

\Bellnumber@{\NVar{n}}
Property / Symbols used: Q12184 / qualifier
 
xml-id: C26.S7.SS1.m1aadec
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.m2adec
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.m1dec
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.m1dec

Latest revision as of 01:12, 2 January 2020

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DLMF:26.7.E2
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    Statements

    B ( n ) = k = 0 n S ( n , k ) , Bell-number 𝑛 superscript subscript 𝑘 0 𝑛 Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle B\left(n\right)=\sum_{k=0}^{n}S\left(n,k\right),}}
    0 references
    DLMF:26.7.E2
    0 references
    B ( n ) Bell-number 𝑛 {\displaystyle{\displaystyle B\left(\NVar{n}\right)}}
    C26.S7.SS1.m1aadec
    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.m2adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C26.S1.XMD4.m1dec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C26.S1.XMD6.m1dec
    0 references