Formula:DLMF:25.12:E8

<< Formula:DLMF:25.12:E7

formula in Polylogarithms

Formula:DLMF:25.12:E9 >>

${\displaystyle{\displaystyle{\displaystyle\sum_{n=1}^{\infty}\frac{\cos\left(n\theta\right)}{n^{2}}=\frac{{\pi^{2}}}{6}-\frac{\pi\theta}{2}+\frac{\theta^{2}}{4}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle 0\leq\theta\leq 2\pi}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2
${\displaystyle{\displaystyle{\displaystyle\pi}}}$ : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4

Bibliography

Equation (8), Section 25.12 of DLMF.

URL links

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