DLMF:24.7.E11 (Q7487): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11288 / rank
 
Normal rank
Property / Symbols used: Q11288 / qualifier
 
Defining formula:

B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}

\BernoullipolyB{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11288 / qualifier
 
xml-id: C24.S2.SS1.m2abdec

Revision as of 01:35, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:24.7.E11
No description defined

    Statements

    Defining formula
    B n ⁡ ( x ) = 1 2 ⁢ π ⁢ i ⁢ ∫ - c - i ⁢ ∞ - c + i ⁢ ∞ ( x + t ) n ⁢ ( π sin ⁡ ( π ⁢ t ) ) 2 ⁢ d t , Bernoulli-polynomial-B 𝑛 𝑥 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 superscript 𝑥 𝑡 𝑛 superscript 𝜋 𝜋 𝑡 2 𝑡 {\displaystyle{\displaystyle B_{n}\left(x\right)=\frac{1}{2\pi i}\int_{-c-i% \infty}^{-c+i\infty}(x+t)^{n}\left(\frac{\pi}{\sin\left(\pi t\right)}\right)^{% 2}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:24.7.E11
    0 references
    constraint
    0 < c < 1 0 𝑐 1 {\displaystyle{\displaystyle 0<c<1}}
    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.m2abdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7487&oldid=32880"