Formula:DLMF:25.6:E12

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Formula:DLMF:25.6:E13 >>

${\displaystyle{\displaystyle{\displaystyle\RiemannZeta^{\prime\prime}@{0}=-\tfrac{1}{2}(\ln\left(2\pi\right))^{2}+\tfrac{1}{2}{\gamma^{2}}-\tfrac{1}{24}{\pi^{2}}+\gamma_{1}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{ln}}}}$ : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
${\displaystyle{\displaystyle{\displaystyle\gamma}}}$ : Euler's constant : http://dlmf.nist.gov/5.2#E3
${\displaystyle{\displaystyle{\displaystyle\gamma_{n}}}}$ : Stieltjes constants : http://drmf.wmflabs.org/wiki/Definition:StieltjesConstants

Bibliography

Equation (12), Section 25.6 of DLMF.

URL links

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