DLMF:24.8.E4 (Q7491): Difference between revisions

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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.m1cdec

Revision as of 01:37, 2 January 2020

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DLMF:24.8.E4
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    Statements

    Defining formula
    E 2 ⁢ n ⁡ ( x ) = ( - 1 ) n ⁢ 4 ⁢ ( 2 ⁢ n ) ! π 2 ⁢ n + 1 ⁢ ∑ k = 0 ∞ sin ⁡ ( ( 2 ⁢ k + 1 ) ⁢ π ⁢ x ) ( 2 ⁢ k + 1 ) 2 ⁢ n + 1 , Euler-polynomial-E 2 𝑛 𝑥 superscript 1 𝑛 4 2 𝑛 superscript 𝜋 2 𝑛 1 superscript subscript 𝑘 0 2 𝑘 1 𝜋 𝑥 superscript 2 𝑘 1 2 𝑛 1 {\displaystyle{\displaystyle E_{2n}\left(x\right)=(-1)^{n}\frac{4(2n)!}{\pi^{2% n+1}}\sum_{k=0}^{\infty}\frac{\sin\left((2k+1)\pi x\right)}{(2k+1)^{2n+1}},}}
    0 references
    DLMF id
    DLMF:24.8.E4
    0 references
    Symbols used
    Q12114
    Defining formula
    E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS2.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1cdec
    0 references
     
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