Finding an English version of Hjortnaes' paper on the series representation of $\zeta(3)$

Question

Hjortnaes published a paper in 1953 establishing the following series representation for $\zeta(3)$, where $\zeta$ is the Riemann Zeta function:

$$ {\displaystyle {\begin{aligned}\zeta (3)&={\frac {5}{2}}\sum _{k=1}^{\infty }(-1)^{k-1}{\frac {k!^{2}}{(2k)!k^{3}}}\\&={\frac {5}{2}}\sum _{k=1}^{\infty }{\frac {(-1)^{k-1}}{{\binom {2k}{k}}k^{3}}}\end{aligned}}} $$

The paper is entitled "Overføring av rekken ${\displaystyle \sum _{k=1}^{\infty }\left({\frac {1}{k^{3}}}\right)}$ til et bestemt integral", and appeared in the Scandinavian Mathematical Society's Proc. 12th Scandinavian Mathematical Congress. Unfortunately the paper is in Norwegian, which I do not understand. A (quick) Google search did not yield any English translations for this paper. Does anyone know where I can find one?

Answer 1

Unfortunately there is no English translation of Hjortnaes' paper. Moreover, after hours of searching I was not able to find Apéry's original paper proving the irrationality of $\zeta(3)$.

However, the following papers give various different proofs of the above identity:

• Lemma 3.1.3 in this paper
• Page 5 in this paper
• A proof by Apéry in this small note
• Van der Poorten's excellent paper, section 3.