DLMF:27.4.E9 (Q8020): Difference between revisions

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Property / constraint
 

s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}

\realpart@@{s}>1
Property / constraint: s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}} / rank
 
Normal rank

Revision as of 17:21, 30 December 2019

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DLMF:27.4.E9
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    Statements

    n = 1 2 ν ( n ) n - s = ( ζ ( s ) ) 2 ζ ( 2 s ) , superscript subscript 𝑛 1 superscript 2 number-of-primes-dividing-nu 𝑛 superscript 𝑛 𝑠 superscript Riemann-zeta 𝑠 2 Riemann-zeta 2 𝑠 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}2^{\nu\left(n\right)}n^{-s}=% \frac{(\zeta\left(s\right))^{2}}{\zeta\left(2s\right)},}}
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    s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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