The acceleration formula for Zeta(, 3, ) is


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

                                              T
                    a(x):=, [a[0](x), a[1](x)] , be defined

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

          and a(x+1)=A(x)a(x), where A(x) is the, 2,  by , 2,  matrix

                     3          2                    3
    (3 x + 5) (x + 1)       (7 x  + 14 x + 4) (x + 1)
[[----------------------, - --------------------------],
                       3                           3
  8 (3 x + 2) (2 x + 3)      12 (3 x + 1) (2 x + 3)

                   3                    3
            (x + 1)              (x + 1)
    [----------------------, - ------------]]
                          3               3
     4 (3 x + 2) (2 x + 3)     8 (2 x + 3)

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

                                      Let

                                                          2
                   a[0](x) (27 x + 19)        a[1](x) (2 x  + 13 x + 11)
        b(x) = 1/8 ------------------- + 1/24 --------------------------
                         3 x + 2                       3 x + 1

                   We have the following acceleration formula

                   (with convergence-rate, 0.003007032652, )

                       infinity            infinity
                        -----               -----
                         \         1         \
                          )     -------- =    )     b(x)
                         /             3     /
                        -----   (z + 1)     -----
                        z = 0               x = 0



                    Proof: The following is a Markov-WZ pair

              3                        3          2                    3
    ((z + x)!)        (3 x + 5) (x + 1)     2 (7 x  + 14 x + 4) (x + 1)
[-----------------, [[------------------, - ----------------------------],
                 3         3 x + 2                  3 (3 x + 1)
 ((2 x + z + 1)!)

              3
     2 (x + 1)           3                                         2         3
    [----------, -(x + 1) ]], [1, z], [(57 + 102 z + 423 x + 1170 x  + 1542 x
      3 x + 2

            5        4       2      4       3        4            2
     + 243 x  + 981 x  + 72 z  + 3 z  + 24 z  + 414 x  z + 378 x z  + 648 x z

             2           3        4        2  2       2  3        3  2
     + 1404 x  z + 99 x z  + 9 x z  + 576 x  z  + 81 x  z  + 270 x  z

             3      /                                     3
     + 1272 x  z)  /  (3 (3 x + 1) (3 x + 2) (2 x + z + 2) ), (22 + 138 z
                  /

                     2          5       2  4        2          3          4
     + 125 x + 1818 x  z + 9 x z  + 81 x  z  + 286 x  + 554 x z  + 126 x z

            3      6       5        4         2  2        2  3         3  2
     + 334 x  + 6 x  + 61 x  + 206 x  + 1872 x  z  + 682 x  z  + 1476 x  z

             3          3  3        5           4          4  2           2
     + 2064 x  z + 276 x  z  + 261 x  z + 1164 x  z + 432 x  z  + 1044 x z

            2                5       4        3    /
     + 216 z  + 795 x z + 6 z  + 48 z  + 148 z )  /  (3 (3 x + 1) (3 x + 2)
                                                 /

                 3
    (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

0.87857980050610299676016105496943487230153930782157291137022258938248182246\

                                                      -78
    32468714388951845892851385945823302809066068764 10