Formula:DLMF:25.6:E15

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Formula:DLMF:25.6:E16 >>

${\displaystyle{\displaystyle{\displaystyle\RiemannZeta^{\prime}@{2n}=\frac{(-1)^{n+1}(2\pi)^{2n}}{2(2n)!}\left(2n\RiemannZeta^{\prime}@{1-2n}-(\psi\left(2n\right)-\ln\left(2\pi\right))\BernoulliB{2n}\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle(-1)}}}$ : negative unity to an integer power : http://dlmf.nist.gov/5.7.E7
${\displaystyle{\displaystyle{\displaystyle\pi}}}$ : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
${\displaystyle{\displaystyle{\displaystyle\psi}}}$ : psi (or digamma) function : http://dlmf.nist.gov/5.2#E2
${\displaystyle{\displaystyle{\displaystyle\mathrm{ln}}}}$ : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
${\displaystyle{\displaystyle{\displaystyle B_{n}}}}$ : Bernoulli polynomial : http://dlmf.nist.gov/24.2#i

Bibliography

Equation (15), Section 25.6 of DLMF.

URL links

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