DLMF:24.8.E3 (Q7490): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
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.m5abdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12113 / rank
 
Normal rank
Property / Symbols used: Q12113 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12113 / qualifier
 
xml-id: C24.S1.XMD2.m1bdec
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.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12112 / rank
 
Normal rank
Property / Symbols used: Q12112 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12112 / qualifier
 
xml-id: C24.S1.XMD7.m1bdec

Latest revision as of 01:36, 2 January 2020

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DLMF:24.8.E3
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    Statements

    B n ( x ) = - n ! ( 2 π i ) n k = - k 0 e 2 π i k x k n . Bernoulli-polynomial-B 𝑛 𝑥 𝑛 superscript 2 𝜋 𝑖 𝑛 superscript subscript 𝑘 𝑘 0 superscript 𝑒 2 𝜋 𝑖 𝑘 𝑥 superscript 𝑘 𝑛 {\displaystyle{\displaystyle B_{n}\left(x\right)=-\frac{n!}{(2\pi i)^{n}}\sum_% {\begin{subarray}{c}k=-\infty\\ k\neq 0\end{subarray}}^{\infty}\frac{e^{2\pi ikx}}{k^{n}}.}}
    0 references
    DLMF:24.8.E3
    0 references
    B n ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    C24.S2.SS1.m2abdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C24.S1.XMD2.m1bdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S1.XMD5.m1bdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C24.S1.XMD7.m1bdec
    0 references