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Formula:8346

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Digital Library of Mathematical Functions ID 25.6.E16

( n + 1 2 ) ⁢ ζ ⁡ ( 2 ⁢ n ) = ∑ k = 1 n - 1 ζ ⁡ ( 2 ⁢ k ) ⁢ ζ ⁡ ( 2 ⁢ n - 2 ⁢ k ) , 𝑛 1 2 Riemann-zeta 2 𝑛 superscript subscript 𝑘 1 𝑛 1 Riemann-zeta 2 𝑘 Riemann-zeta 2 𝑛 2 𝑘 {\displaystyle{\displaystyle\left(n+\tfrac{1}{2}\right)\zeta\left(2n\right)=% \sum_{k=1}^{n-1}\zeta\left(2k\right)\zeta\left(2n-2k\right),}}


Constraint(s)

n ≥ 2 𝑛 2 {\displaystyle{\displaystyle n\geq 2}}

Symbols List

  • ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}} : Riemann zeta function
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
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This page was last edited on 28 January 2024, at 11:02.
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