View source for Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n)

==Theorem==
The following formula holds for $|z|<\pi$:
$$z \mathrm{coth}(z) = 2 \displaystyle\sum_{k=0}^{\infty} (-1)^{k+1} \zeta(2k) \dfrac{z^{2k}}{\pi^{2k}},$$
where $\mathrm{coth}$ denotes [[coth|hyperbolic cotangent]], $\zeta$ denotes [[Riemann zeta]], and $\pi$ denotes [[pi]].

==Proof==

==References==
* {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)!|next=findme}}: $\S 1.20 (2)$

[[Category:Theorem]]
[[Category:Unproven]]