Formula:DLMF:25.2:E7

<< Formula:DLMF:25.2:E6

formula in Definition and Expansions

Formula:DLMF:25.2:E8 >>

${\displaystyle{\displaystyle{\displaystyle\RiemannZeta^{(k)}@{s}=(-1)^{k}\sum_{n=2}^{\infty}(\ln n)^{k}n^{-s}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\Re{s}>1}}}$ &
${\displaystyle{\displaystyle{\displaystyle k=1,2,3,\dots}}}$

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

& : logical and
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : 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
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : 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 (7), Section 25.2 of DLMF.

URL links

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

<< Formula:DLMF:25.2:E6

formula in Definition and Expansions

Formula:DLMF:25.2:E8 >>