DLMF:24.13.E5 (Q7539): Difference between revisions

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‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11238 / rank
 
Normal rank
Property / Symbols used: Q11238 / qualifier
 
Defining formula:

E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}

\EulernumberE{\NVar{n}}
Property / Symbols used: Q11238 / qualifier
 
xml-id: C24.S2.SS2.m1adec

Revision as of 01:43, 2 January 2020

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DLMF:24.13.E5
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    Statements

    Defining formula
    ∫ 1 / 4 3 / 4 B n ⁡ ( t ) ⁢ d t = E n 2 2 ⁢ n + 1 . superscript subscript 1 4 3 4 Bernoulli-polynomial-B 𝑛 𝑡 𝑡 Euler-number-E 𝑛 superscript 2 2 𝑛 1 {\displaystyle{\displaystyle\int_{1/4}^{3/4}B_{n}\left(t\right)\mathrm{d}t=% \frac{E_{n}}{2^{2n+1}}.}}
    0 references
    DLMF id
    DLMF:24.13.E5
    0 references
    Symbols used
    Q11288
    Defining formula
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2addec
    0 references
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1adec
    0 references
     
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