Formula:DLMF:25.6:E18

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formula in Integer Arguments

Formula:DLMF:25.6:E19 >>

${\displaystyle{\displaystyle{\displaystyle{\left(n+\tfrac{1}{4}\right)\RiemannZeta@{4n}+\tfrac{1}{2}(\RiemannZeta@{2n})^{2}=\sum_{k=1}^{n}\RiemannZeta@{2k}\RiemannZeta@{4n-2k}}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle n\geq 1}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation (18), Section 25.6 of DLMF.

URL links

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