DLMF:26.7.E5 (Q7821)

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DLMF:26.7.E5
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    Statements

    Defining formula
    ∑ n = 0 ∞ B ⁡ ( n ) ⁢ x n n ! = exp ⁡ ( e x - 1 ) . superscript subscript 𝑛 0 Bell-number 𝑛 superscript 𝑥 𝑛 𝑛 𝑥 1 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}B\left(n\right)\frac{x^{n}}{n!}% =\exp({\mathrm{e}^{x}}-1).}}
    0 references
    DLMF id
    DLMF:26.7.E5
    0 references
    Symbols used
    Q12184
    Defining formula
    B ⁡ ( n ) Bell-number 𝑛 {\displaystyle{\displaystyle B\left(\NVar{n}\right)}}
    xml-id
    C26.S7.SS1.m1aedec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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