Formula:DLMF:25.2:E6

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formula in Definition and Expansions

Formula:DLMF:25.2:E7 >>

${\displaystyle{\displaystyle{\displaystyle\RiemannZeta^{\prime}@{s}=-\sum_{n=2}^{\infty}(\ln n)n^{-s}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\Re{s}>1}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle\mathrm{ln}}}}$ : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
${\displaystyle{\displaystyle{\displaystyle\Re{z}}}}$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation (6), Section 25.2 of DLMF.

URL links

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