New revision: **Convergence acceleration technique of the value of the function $\zeta(s)$ at $s=4$ (or the value of $\eta(s)$ at $s=4$) using creative telescoping/Zeilberger's algorithm?**
>Is it already kown if the $\zeta(4)$ accelerated convergence series
$$\zeta(4):=\sum_{n=1}^{\infty }\frac{1}{n^{4}}=\frac{36}{17}\sum_{1}^{\infty }
\frac{1}{n^{4}\binom{2n}{n}}\tag{1}$$
(proved e.g. in [1, Corollaire 5.3]) can be obtained by a similar technique to those described in [2, §1], where the defining series for $\zeta(3),\zeta(2)$ are accelerated yielding these equalities?
>Is it already kown if the $\zeta(4)$ accelerated convergence series
$$\zeta(4):=\sum_{n=1}^{\infty }\frac{1}{n^{4}}=\frac{36}{17}\sum_{1}^{\infty }
\frac{1}{n^{4}\binom{2n}{n}}\tag{1}$$
(proved e.g. in [1, Corollaire 5.3]) can be obtained by a similar technique to those described in [2, §1], where the defining series for $\zeta(3),\zeta(2)$ are accelerated yielding these equalities?
Convergence acceleration technique of the value of the function $\zeta(s)$ at $s=4$ (or the value of $\eta(s)$ at $s=4$) using creative telescoping/Zeilberger's algorithm?
Is it already kown if the $\zeta(4)$ accelerated convergence series
$$\zeta(4):=\sum_{n=1}^{\infty }\frac{1}{n^{4}}=\f...
