Does anybody know whether the $\zeta(4)$ accelerated series mencioned on section 10 of Alf van der poorten's paper A proof that Euler missed ..., transcribed at
ega-math.narod.ru/Apery1.htm, can be obtain by similar techniques of those used in the same paper to derive the corresponding accelerated series for $\zeta(3),\zeta(2)$? Remark: there's a 1981 paper by Henri Cohen availble at numdam, where he used the Euler-Maclaurin summation to prove that accelerated formula for $\zeta(4)$.
