2
$\begingroup$

This have been asked on MSE but got no answers.

I'm searching for a proof that $\pi$ is irrational using a series representation for $\pi$, but can't find it.

However, on this wikipedia page show's that Apery's proof on the irrationality of $\zeta(3)$ can be simplified to apply on $\zeta(2)$ which is better than what i'm looking for because it shows that $\pi^2$ is irrational. But I can't find this proof either. If it's was done, maybe no one ever published.

$\endgroup$
  • $\begingroup$ Check out van der Poorten's survey on Apery's proof "A proof that Euler missed" in Math. Intelligencer, as far as I remember it does $\zeta(2)$ as well. $\endgroup$ – Piotr Achinger May 16 at 3:33
1
$\begingroup$

Beukers gave a proof of the irrationality of $\zeta(2)$ and $\zeta(3)$ using Apery's ideas, expressed in integral form here. This was published in 1979.

$\endgroup$
  • $\begingroup$ I've seen that but I'm interessed in proof's that uses fast convergent series. $\endgroup$ – Pinteco May 16 at 3:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.