DLMF:24.4.E20 (Q7433)

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DLMF:24.4.E20
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    Statements

    Defining formula
    E n ⁡ ( m ⁢ x ) = m n ⁢ ∑ k = 0 m - 1 ( - 1 ) k ⁢ E n ⁡ ( x + k m ) , Euler-polynomial-E 𝑛 𝑚 𝑥 superscript 𝑚 𝑛 superscript subscript 𝑘 0 𝑚 1 superscript 1 𝑘 Euler-polynomial-E 𝑛 𝑥 𝑘 𝑚 {\displaystyle{\displaystyle E_{n}\left(mx\right)=m^{n}\sum_{k=0}^{m-1}(-1)^{k% }E_{n}\left(x+\frac{k}{m}\right),}}
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    DLMF id
    DLMF:24.4.E20
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    constraint
    m = 1 , 3 , 5 , … 𝑚 1 3 5 … {\displaystyle{\displaystyle m=1,3,5,\dots}}
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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.m2ahdec
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    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1mdec
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    Q12115
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1gdec
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    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1sdec
    0 references
    Q12112
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1kdec
    0 references
     
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