DLMF:24.4.E9 (Q7422)

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DLMF:24.4.E9
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    Statements

    Defining formula
    ∑ k = 0 m - 1 ( a + d ⁢ k ) n = d n n + 1 ⁢ ( B n + 1 ⁡ ( m + a d ) - B n + 1 ⁡ ( a d ) ) , superscript subscript 𝑘 0 𝑚 1 superscript 𝑎 𝑑 𝑘 𝑛 superscript 𝑑 𝑛 𝑛 1 Bernoulli-polynomial-B 𝑛 1 𝑚 𝑎 𝑑 Bernoulli-polynomial-B 𝑛 1 𝑎 𝑑 {\displaystyle{\displaystyle\sum_{k=0}^{m-1}(a+dk)^{n}={\frac{d^{n}}{n+1}\left% (B_{n+1}\left(m+\frac{a}{d}\right)-B_{n+1}\left(\frac{a}{d}\right)\right)},}}
    0 references
    DLMF id
    DLMF:24.4.E9
    0 references
    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.m2addec
    0 references
     
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