DLMF:24.8.E5 (Q7492)

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DLMF:24.8.E5
No description defined

    Statements

    Defining formula
    E 2 ⁢ n - 1 ⁡ ( x ) = ( - 1 ) n ⁢ 4 ⁢ ( 2 ⁢ n - 1 ) ! π 2 ⁢ n ⁢ ∑ k = 0 ∞ cos ⁡ ( ( 2 ⁢ k + 1 ) ⁢ π ⁢ x ) ( 2 ⁢ k + 1 ) 2 ⁢ n . Euler-polynomial-E 2 𝑛 1 𝑥 superscript 1 𝑛 4 2 𝑛 1 superscript 𝜋 2 𝑛 superscript subscript 𝑘 0 2 𝑘 1 𝜋 𝑥 superscript 2 𝑘 1 2 𝑛 {\displaystyle{\displaystyle E_{2n-1}\left(x\right)=(-1)^{n}\frac{4(2n-1)!}{% \pi^{2n}}\sum_{k=0}^{\infty}\frac{\cos\left((2k+1)\pi x\right)}{(2k+1)^{2n}}.}}
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    DLMF id
    DLMF:24.8.E5
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    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.m2aadec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
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    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1ddec
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    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1ddec
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    Q12112
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1ddec
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