DLMF:26.7.E4 (Q7820): 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.m1acdec

Revision as of 01:13, 2 January 2020

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DLMF:26.7.E4
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    Statements

    B ( n ) = e - 1 k = 1 k n k ! = 1 + e - 1 k = 1 2 n k n k ! . Bell-number 𝑛 1 superscript subscript 𝑘 1 superscript 𝑘 𝑛 𝑘 1 1 superscript subscript 𝑘 1 2 𝑛 superscript 𝑘 𝑛 𝑘 {\displaystyle{\displaystyle B\left(n\right)={\mathrm{e}^{-1}}\sum_{k=1}^{% \infty}\frac{k^{n}}{k!}=1+\left\lfloor{\mathrm{e}^{-1}}\sum_{k=1}^{2n}\frac{k^% {n}}{k!}\right\rfloor.}}
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    DLMF:26.7.E4
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    B ( n ) Bell-number 𝑛 {\displaystyle{\displaystyle B\left(\NVar{n}\right)}}
    C26.S7.SS1.m1acdec
    0 references