DLMF:26.7.E3 (Q7819)

From DRMF
Revision as of 01:12, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7819&oldid=30001"