  In this paper we introduce and study double tails of multiple zeta values. We
show, in particular, that they satisfy certain recurrence relations and deduce
from this a generalization of Euler's classical formula
$\zeta(2)=3\sum_{m=1}^\infty m^{-2}\left({2m\atop m}\right)^{-1}$ to all
multiple zeta values, as well as a new and very efficient algorithm for
computing these values.
