Formula:DLMF:25.6:E15

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

Constraint(s)

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

Proof

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Symbols List

: Riemann zeta function : http://dlmf.nist.gov/25.2#E1
: negative unity to an integer power : http://dlmf.nist.gov/5.7.E7
: ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
: psi (or digamma) function : http://dlmf.nist.gov/5.2#E2
: principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
: Bernoulli polynomial : http://dlmf.nist.gov/24.2#i

URL links

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