DLMF:24.2.E1 (Q7398): 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.m2adec
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.m5adec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q12111 / rank
 
Normal rank
Property / Symbols used: Q12111 / qualifier
 
Defining formula:

t 𝑡 {\displaystyle{\displaystyle t}}

t
Property / Symbols used: Q12111 / qualifier
 
xml-id: C24.S1.XMD6.m1dec

Latest revision as of 01:23, 2 January 2020

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English
DLMF:24.2.E1
No description defined

    Statements

    t e t - 1 = n = 0 B n t n n ! , 𝑡 superscript 𝑒 𝑡 1 superscript subscript 𝑛 0 Bernoulli-number-B 𝑛 superscript 𝑡 𝑛 𝑛 {\displaystyle{\displaystyle\frac{t}{e^{t}-1}=\sum_{n=0}^{\infty}B_{n}\frac{t^% {n}}{n!},}}
    0 references
    DLMF:24.2.E1
    0 references
    | t | < 2 π 𝑡 2 𝜋 {\displaystyle{\displaystyle|t|<2\pi}}
    0 references
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    C24.S2.SS1.m1adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S1.XMD5.m1dec
    0 references
    t 𝑡 {\displaystyle{\displaystyle t}}
    C24.S1.XMD6.m1dec
    0 references