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DLMF:27.4.E9

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Formula:8713
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MaRDI QIDQ8713

  • Label: DLMF:27.4.E9


Digital Library of Mathematical Functions ID 27.4.E9

∑ 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)},}}


Constraint(s)

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

Symbols List

  • ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}} : Riemann zeta function
  • ν ⁡ ( n ) number-of-primes-dividing-nu 𝑛 {\displaystyle{\displaystyle\nu\left(\NVar{n}\right)}} :
  • ℜ ⁡ absent {\displaystyle{\displaystyle\Re}} : real part
  • n 𝑛 {\displaystyle{\displaystyle n}} : positive integer
  •  Edit this on Wikidata

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