DLMF:24.13.E4 (Q7538): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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.m1cdec

Latest revision as of 01:43, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:24.13.E4
No description defined

    Statements

    Defining formula
    ∫ 0 1 / 2 B n ⁡ ( t ) ⁢ d t = 1 - 2 n + 1 2 n ⁢ B n + 1 n + 1 , superscript subscript 0 1 2 Bernoulli-polynomial-B 𝑛 𝑡 𝑡 1 superscript 2 𝑛 1 superscript 2 𝑛 Bernoulli-number-B 𝑛 1 𝑛 1 {\displaystyle{\displaystyle\int_{0}^{1/2}B_{n}\left(t\right)\mathrm{d}t=\frac% {1-2^{n+1}}{2^{n}}\frac{B_{n+1}}{n+1},}}
    0 references
    DLMF id
    DLMF:24.13.E4
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
    0 references
    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.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1cdec
    0 references
    Q12111
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7538&oldid=34085"