DLMF:24.4.E19 (Q7432)

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DLMF:24.4.E19
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    Statements

    Defining formula
    E n ⁡ ( m ⁢ x ) = - 2 ⁢ m n n + 1 ⁢ ∑ k = 0 m - 1 ( - 1 ) k ⁢ B n + 1 ⁡ ( x + k m ) , Euler-polynomial-E 𝑛 𝑚 𝑥 2 superscript 𝑚 𝑛 𝑛 1 superscript subscript 𝑘 0 𝑚 1 superscript 1 𝑘 Bernoulli-polynomial-B 𝑛 1 𝑥 𝑘 𝑚 {\displaystyle{\displaystyle E_{n}\left(mx\right)=-\frac{2m^{n}}{n+1}\sum_{k=0% }^{m-1}(-1)^{k}B_{n+1}\left(x+\frac{k}{m}\right),}}
    0 references
    DLMF id
    DLMF:24.4.E19
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    constraint
    m = 2 , 4 , 6 , … 𝑚 2 4 6 … {\displaystyle{\displaystyle m=2,4,6,\dots}}
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    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.m2agdec
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    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.m2agdec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1ldec
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    Q12115
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1fdec
    0 references
     
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