DLMF:26.8.E12 (Q7837): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12173 / rank
 
Normal rank
Property / Symbols used: Q12173 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12173 / qualifier
 
xml-id: C26.S1.XMD1.m1edec

Revision as of 12:53, 2 January 2020

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English
DLMF:26.8.E12
No description defined

    Statements

    test
    ∑ n = 0 ∞ S ⁡ ( n , k ) ⁢ x n n ! = ( e x - 1 ) k k ! , superscript subscript 𝑛 0 Stirling-number-second-kind-S 𝑛 𝑘 superscript 𝑥 𝑛 𝑛 superscript 𝑥 1 𝑘 𝑘 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}S\left(n,k\right)\frac{x^{n}}{n% !}=\frac{({\mathrm{e}^{x}}-1)^{k}}{k!},}}
    0 references
    DLMF id
    DLMF:26.8.E12
    0 references
    Symbols used
    Q12131
    test
    S ⁡ ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p3.m2afdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q12173
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C26.S1.XMD1.m1edec
    0 references
     
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