  With this paper we introduce a new series representation of $\zeta(3)$, which
is based on the Clausen representation of odd integer zeta values. Although,
relatively fast converging series based on the Clausen representation exist for
$\zeta(3)$, their convergence behavior is very slow compared to BBP-type
formulas, and as a consequence they are not used for explicit numerical
computations. The reason is found in the fact that the corresponding Clausen
function can be calculated analytically for a few rational arguments only,
where $x=\frac{1}{6}$ is the smallest one. Using polylogarithmic identities in
combination with a polynomial description of the even Bernoulli numbers, the
convergence behavior of the Clausen-type representation has been improved to a
level that allows us to challenge ultimately all BBP-type formulas available
for $\zeta(3)$. We present an explicit numerical comparison between one of the
best available BBP formulas and our formalism. Furthermore, we demonstrate by
an explicit computation using the first four terms in our series representation
only that $\zeta(3)$ results with an accuracy of $2*10^{-26}$, where our
computation guarantees on each approximation level for an analytical expression
for $\zeta(3)$.
