Formula:DLMF:25.8:E8

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${\displaystyle{\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{% \RiemannZeta@{2k}}{k}z^{2k}=\ln@{\frac{\pi z}{\sin@{\pi z}}}}}}$

Constraint(s)

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

Proof

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Symbols List

: sum : http://drmf.wmflabs.org/wiki/Definition:sum
: Riemann zeta function : http://dlmf.nist.gov/25.2#E1
: principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
: ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
: sine function : http://dlmf.nist.gov/4.14#E1

URL links

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