DLMF:24.8.E2 (Q7489): Difference between revisions

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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.m1adec

Revision as of 01:36, 2 January 2020

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DLMF:24.8.E2
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    Statements

    Defining formula
    B 2 ⁢ n + 1 ⁡ ( x ) = ( - 1 ) n + 1 ⁢ 2 ⁢ ( 2 ⁢ n + 1 ) ! ( 2 ⁢ π ) 2 ⁢ n + 1 ⁢ ∑ k = 1 ∞ sin ⁡ ( 2 ⁢ π ⁢ k ⁢ x ) k 2 ⁢ n + 1 . Bernoulli-polynomial-B 2 𝑛 1 𝑥 superscript 1 𝑛 1 2 2 𝑛 1 superscript 2 𝜋 2 𝑛 1 superscript subscript 𝑘 1 2 𝜋 𝑘 𝑥 superscript 𝑘 2 𝑛 1 {\displaystyle{\displaystyle B_{2n+1}\left(x\right)=(-1)^{n+1}\frac{2(2n+1)!}{% (2\pi)^{2n+1}}\sum_{k=1}^{\infty}\frac{\sin\left(2\pi kx\right)}{k^{2n+1}}.}}
    0 references
    DLMF id
    DLMF:24.8.E2
    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.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1adec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1adec
    0 references
     
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