View source for Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)!

==Theorem==
The following formula holds for $|z| < \pi$: 
$$z \mathrm{coth}(z) = \displaystyle\sum_{k=0}^{\infty} 2^{2k} B_{2k} \dfrac{z^{2k}}{(2k)!},$$
where $\mathrm{coth}$ denotes [[coth|hyperbolic cotangent]], $B_{2k}$ denotes [[Bernoulli numbers]], and $(2k)!$ denotes [[factorial]].

==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) = 2z/(e^(2z)-1) + z|next=Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n)}}: $\S 1.20 (2)$

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