DLMF:27.4.E11 (Q8022): Difference between revisions

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Property / constraint
 

s > max ( 1 , 1 + α ) 𝑠 1 1 𝛼 {\displaystyle{\displaystyle\Re s>\max(1,1+\Re\alpha)}}

\realpart@@{s}>\max(1,1+\realpart@@{\alpha})
Property / constraint: s > max ( 1 , 1 + α ) 𝑠 1 1 𝛼 {\displaystyle{\displaystyle\Re s>\max(1,1+\Re\alpha)}} / rank
 
Normal rank

Revision as of 17:21, 30 December 2019

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DLMF:27.4.E11
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    Statements

    n = 1 σ α ( n ) n - s = ζ ( s ) ζ ( s - α ) , superscript subscript 𝑛 1 divisor-sigma 𝛼 𝑛 superscript 𝑛 𝑠 Riemann-zeta 𝑠 Riemann-zeta 𝑠 𝛼 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\sigma_{\alpha}\left(n\right)n^% {-s}=\zeta\left(s\right)\zeta\left(s-\alpha\right),}}
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    s > max ( 1 , 1 + α ) 𝑠 1 1 𝛼 {\displaystyle{\displaystyle\Re s>\max(1,1+\Re\alpha)}}
    0 references