DLMF:26.7.E5 (Q7821): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec
Property / Symbols used
 
Property / Symbols used: Q12173 / rank
 
Normal rank
Property / Symbols used: Q12173 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12173 / qualifier
 
xml-id: C26.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1ddec

Latest revision as of 01:13, 2 January 2020

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English
DLMF:26.7.E5
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    Statements

    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:26.7.E5
    0 references
    B ( n ) Bell-number 𝑛 {\displaystyle{\displaystyle B\left(\NVar{n}\right)}}
    C26.S7.SS1.m1aedec
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    exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    C4.S2.E19.m2adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C26.S1.XMD1.m1dec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C26.S1.XMD6.m1ddec
    0 references