Formula:DLMF:25.8:E6

<< Formula:DLMF:25.8:E5

formula in Sums

Formula:DLMF:25.8:E7 >>

${\displaystyle{\displaystyle{\displaystyle\sum_{k=0}^{\infty}\RiemannZeta@{2k}z^{2k}=-\tfrac{1}{2}\pi z\cot\left(\pi z\right)}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle|z|<1}}}$

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

${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
${\displaystyle{\displaystyle{\displaystyle\pi}}}$ : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
${\displaystyle{\displaystyle{\displaystyle\mathrm{cot}}}}$ : cotangent function : http://dlmf.nist.gov/4.14#E7

Bibliography

Equation (6), Section 25.8 of DLMF.

URL links

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

<< Formula:DLMF:25.8:E5

formula in Sums

Formula:DLMF:25.8:E7 >>