# Extending the Basel problem for 1/n^4 [duplicate]

Is there any way to prove that:

$$\sum_{n=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90}$$

Using Euler's original proof of equating coefficients?

## marked as duplicate by Adam Hughes, Parcly Taxel, user91500, Pragabhava, user223391 Oct 30 '16 at 20:55

• See 1st comment there for a derivation from $\frac{\pi^2}{\sin^2(\pi z)} = \sum_{n=-\infty}^\infty \frac{1}{(z-n)^2}$ – reuns Oct 30 '16 at 15:44
• Someone knows if Euler could prove that $\pi \cot(z) = \lim_{N \to \infty}\sum_{n=-N}^N\frac{1}{z-n}$ without making some complicated digressions about $\frac{\sin(\pi x)}{ x}$ Weierstrass product ? I think he had some problems because he wasn't thinking to meromorphic functions of $z \in \mathbb{C}$ – reuns Oct 30 '16 at 15:49