Formula:DLMF:25.6:E3

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formula in Integer Arguments

Formula:DLMF:25.6:E4 >>

${\displaystyle{\displaystyle{\displaystyle\RiemannZeta@{-n}=-\frac{\BernoulliB{n+1}}{n+1}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle n=1,2,3,\dots}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
${\displaystyle{\displaystyle{\displaystyle B_{n}}}}$ : Bernoulli polynomial : http://dlmf.nist.gov/24.2#i

Bibliography

Equation (3), Section 25.6 of DLMF.

URL links

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