DLMF:27.11.E5 (Q8074)

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DLMF:27.11.E5
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    Statements

    Defining formula
    ∑ n ≤ x σ α ⁡ ( n ) = ζ ⁡ ( α + 1 ) α + 1 ⁢ x α + 1 + O ⁡ ( x β ) , subscript 𝑛 𝑥 divisor-sigma 𝛼 𝑛 Riemann-zeta 𝛼 1 𝛼 1 superscript 𝑥 𝛼 1 Big-O superscript 𝑥 𝛽 {\displaystyle{\displaystyle\sum_{n\leq x}\sigma_{\alpha}\left(n\right)=\frac{% \zeta\left(\alpha+1\right)}{\alpha+1}x^{\alpha+1}+O\left(x^{\beta}\right),}}
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    DLMF id
    DLMF:27.11.E5
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    constraint
    β = max ⁡ ( 1 , α ) 𝛽 1 𝛼 {\displaystyle{\displaystyle\beta=\max(1,\alpha)}}
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