DLMF:24.4.E10 (Q7423)

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DLMF:24.4.E10
No description defined

    Statements

    Defining formula
    ∑ k = 0 m - 1 ( - 1 ) k ⁢ ( a + d ⁢ k ) n = d n 2 ⁢ ( ( - 1 ) m - 1 ⁢ E n ⁡ ( m + a d ) + E n ⁡ ( a d ) ) . superscript subscript 𝑘 0 𝑚 1 superscript 1 𝑘 superscript 𝑎 𝑑 𝑘 𝑛 superscript 𝑑 𝑛 2 superscript 1 𝑚 1 Euler-polynomial-E 𝑛 𝑚 𝑎 𝑑 Euler-polynomial-E 𝑛 𝑎 𝑑 {\displaystyle{\displaystyle\sum_{k=0}^{m-1}(-1)^{k}(a+dk)^{n}={\frac{d^{n}}{2% }\left((-1)^{m-1}E_{n}\left(m+\frac{a}{d}\right)+E_{n}\left(\frac{a}{d}\right)% \right)}.}}
    0 references
    DLMF id
    DLMF:24.4.E10
    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.m2addec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1cdec
    0 references
    Q12115
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1cdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1idec
    0 references
     
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