Formula:DLMF:25.16:E10

<< Formula:DLMF:25.16:E9

formula in Mathematical Applications

Formula:DLMF:25.16:E11 >>

${\displaystyle{\displaystyle{\displaystyle\EulerSumH@{-2a}=\frac{1}{2}\RiemannZeta@{1-2a}=-\frac{\BernoulliB{2a}}{4a}}}}$

Constraint(s)

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

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle H}}}$ : Euler sums : http://dlmf.nist.gov/25.16#SS2.p1
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : 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 (10), Section 25.16 of DLMF.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:DLMF:25.16:E9

formula in Mathematical Applications

Formula:DLMF:25.16:E11 >>