Hypergeometric Series Acceleration Via the WZ method
  Based on the WZ method, some series acceleration formulas are given. These formulas allow to write down an infinite family of parametrized identities from any given identity of WZ type. Further, this family, in the case of the Riemann Zeta function, gives rise to many accelerated expressions for $\zeta(3)$.   The present method produced a formula, given at the end of the paper, that was used recently Sebastian Wedeniwski to compute Apery's constant to more than 32 million digits, holding the present record! 
Tewodros Amdeberhan (Temple University), Doron Zeilberger