The acceleration formula for Zeta(, 2, ) is

               Theorem.  Let the column-vector of functions of, x

                                         T
                        a(x):=, [a[0](x)] , be defined

                                                          T
                    by the initial conditions:, a(0) = [1]

          and a(x+1)=A(x)a(x), where A(x) is the, 1,  by , 1,  matrix

                                           3
                                    (x + 1)
                           [[----------------------]]
                                                  2
                             8 (2 x + 1) (2 x + 3)

                                                                 T
              In other words, a(x)=A(x-1)A(x-2)...A(0) times, [1]

                                      Let

                                    a[0](x) (21 x + 13)
                         b(x) = 1/8 -------------------
                                          2 x + 1

                   We have the following acceleration formula

                    (with convergence-rate, 0.01562500000, )

                       infinity            infinity
                        -----               -----
                         \         1         \
                          )     -------- =    )     b(x)
                         /             2     /
                        -----   (z + 1)     -----
                        z = 0               x = 0



                    Proof: The following is a Markov-WZ pair

              2               3
    ((z + x)!)         (x + 1)                  3       2                   2
[-----------------, [[-----------]], [1], [(21 x  + 55 x  + 47 x + 13 + 28 x  z
                 2    2 (2 x + 1)
 ((2 x + z + 1)!)

                             2       2      3    /                           2
     + 48 x z + 20 z + 13 x z  + 11 z  + 2 z )  /  (2 (2 x + 1) (2 x + z + 2) )
                                               /

    ]]

                                    (check!)

      Now use formula (Acc) in the human-paper The Markov-WZ Method, QED

                         The error in using 30 terms is

-0.3343737970446460912796691139964154932428091881891989008241668484695012330\
    9613394414567090770963931570659434576646834817662842065893578760319432

      -56
    10