DLMF:24.7.E5 (Q7481): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12111 / rank
 
Normal rank
Property / Symbols used: Q12111 / qualifier
 
test:

t 𝑡 {\displaystyle{\displaystyle t}}

t
Property / Symbols used: Q12111 / qualifier
 
xml-id: C24.S1.XMD6.m1ddec

Latest revision as of 00:34, 2 January 2020

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DLMF:24.7.E5
No description defined

    Statements

    test
    B 2 ⁢ n = ( - 1 ) n ⁢ 2 ⁢ n ⁢ ( 2 ⁢ n - 1 ) π ⁢ ∫ 0 ∞ t 2 ⁢ n - 2 ⁢ ln ⁡ ( 1 - e - 2 ⁢ π ⁢ t ) ⁢ d t . Bernoulli-number-B 2 𝑛 superscript 1 𝑛 2 𝑛 2 𝑛 1 𝜋 superscript subscript 0 superscript 𝑡 2 𝑛 2 1 superscript 𝑒 2 𝜋 𝑡 𝑡 {\displaystyle{\displaystyle B_{2n}=(-1)^{n}\frac{2n(2n-1)}{\pi}\*\int_{0}^{% \infty}t^{2n-2}\ln\left(1-e^{-2\pi t}\right)\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:24.7.E5
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1addec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q12110
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1ddec
    0 references
    Q12111
    test
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1ddec
    0 references
     
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