DLMF:26.7.E3 (Q7819): Difference between revisions

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Property / constraint
 

m ≥ n 𝑚 𝑛 {\displaystyle{\displaystyle m\geq n}}

m\geq n
Property / constraint: m ≥ n 𝑚 𝑛 {\displaystyle{\displaystyle m\geq n}} / rank
 
Normal rank
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.m1abdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
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.m1dec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q12171 / rank
 
Normal rank
Property / Symbols used: Q12171 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12171 / qualifier
 
xml-id: C26.S1.XMD5.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.m1adec

Latest revision as of 01:12, 2 January 2020

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English
DLMF:26.7.E3
No description defined

    Statements

    Defining formula
    B ⁡ ( n ) = ∑ k = 1 m k n k ! ⁢ ∑ j = 0 m - k ( - 1 ) j j ! , Bell-number 𝑛 superscript subscript 𝑘 1 𝑚 superscript 𝑘 𝑛 𝑘 superscript subscript 𝑗 0 𝑚 𝑘 superscript 1 𝑗 𝑗 {\displaystyle{\displaystyle B\left(n\right)=\sum_{k=1}^{m}\frac{k^{n}}{k!}% \sum_{j=0}^{m-k}\frac{(-1)^{j}}{j!},}}
    0 references
    DLMF id
    DLMF:26.7.E3
    0 references
    constraint
    m ≥ n 𝑚 𝑛 {\displaystyle{\displaystyle m\geq n}}
    0 references
    Symbols used
    Q12184
    Defining formula
    B ⁡ ( n ) Bell-number 𝑛 {\displaystyle{\displaystyle B\left(\NVar{n}\right)}}
    xml-id
    C26.S7.SS1.m1abdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1dec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1adec
    0 references
    Q12171
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C26.S1.XMD5.m1dec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1adec
    0 references
     
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