  Inspired by the results of Rhin and Viola (2001), the purpose of this work is
to elaborate on a series representation for $\zeta \left( 3\right)$ which only
depends on one single integer parameter. This is accomplished by deducing a
Hermite-Pad\'e approximation problem using ideas of Sorokin (1998). As a
consequence we get a new recurrence relation for the approximation of
$\zeta(3)$ as well as a corresponding new continued fraction expansion for
$\zeta(3)$, which do no reproduce Ap\'ery's phenomenon, i.e., though the
approaches are different, they lead to the same sequence of diophantine
approximations to $\zeta \left( 3\right) $. Finally, the convergence rates of
several series representations of $\zeta(3)$ are compared.
