DLMF:26.7.E7 (Q7824)

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DLMF:26.7.E7
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    Statements

    Defining formula
    B ⁡ ( n ) = N n ⁢ e N - n - 1 ( 1 + ln ⁡ N ) 1 / 2 ⁢ ( 1 + O ⁡ ( ( ln ⁡ n ) 1 / 2 n 1 / 2 ) ) , Bell-number 𝑛 superscript 𝑁 𝑛 𝑁 𝑛 1 superscript 1 𝑁 1 2 1 Big-O superscript 𝑛 1 2 superscript 𝑛 1 2 {\displaystyle{\displaystyle B\left(n\right)=\frac{N^{n}{\mathrm{e}^{N-n-1}}}{% (1+\ln N)^{1/2}}\left(1+O\left(\frac{(\ln n)^{1/2}}{n^{1/2}}\right)\right),}}
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    DLMF id
    DLMF:26.7.E7
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    constraint
    n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}
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    Symbols used
    Q12184
    Defining formula
    B ⁡ ( n ) Bell-number 𝑛 {\displaystyle{\displaystyle B\left(\NVar{n}\right)}}
    xml-id
    C26.S7.SS1.m1agdec
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