The acceleration formula for Zeta(, 4, ) is


                  2                     3
    1        (23 x  + 76 x + 63) (x + 1)
[--------, [[----------------------------,
        4                            4
 (z + 1)       32 (3 + 4 x) (2 x + 3)

            4        3         2                       3
      (150 x  + 670 x  + 1041 x  + 652 x + 141) (x + 1)
    - --------------------------------------------------,
                                              4
              64 (3 + 4 x) (2 x + 1) (2 x + 3)

          6         5          4          3         2                        3
    (900 x  + 4870 x  + 10211 x  + 10534 x  + 5629 x  + 1470 x + 144) (x + 1)

       /                                            4
      /  (64 (2 x + 1) (1 + 4 x) (3 + 4 x) (2 x + 3) )], [
     /

                        3           3        2                      3
     5 (3 x + 5) (x + 1)       (94 x  + 266 x  + 215 x + 53) (x + 1)
    -----------------------, - --------------------------------------,
                          4                                      4
    16 (3 + 4 x) (2 x + 3)       32 (3 + 4 x) (2 x + 1) (2 x + 3)

          5         4         3         2                      3
    (540 x  + 2040 x  + 2778 x  + 1732 x  + 495 x + 51) (x + 1)
    ------------------------------------------------------------], [
                                                      4
            32 (2 x + 1) (1 + 4 x) (3 + 4 x) (2 x + 3)

                   3                               3
          5 (x + 1)             5 (2 + 3 x) (x + 1)
    -----------------------, - -----------------------,
                          4                          4
    16 (3 + 4 x) (2 x + 3)     32 (3 + 4 x) (2 x + 3)

         3        2                    3
    (82 x  + 133 x  + 65 x + 9) (x + 1)      135 x + 103
    ------------------------------------]], [------------,
                                     4       32 (3 + 4 x)
     32 (1 + 4 x) (3 + 4 x) (2 x + 3)

        3       2                    5        4    3        2
    10 x  + 52 x  + 67 x + 25    60 x  + 150 x  - x  - 265 x  - 234 x - 60
    -------------------------, - -----------------------------------------],
     64 (3 + 4 x) (2 x + 1)          64 (2 x + 1) (1 + 4 x) (3 + 4 x)

    0.0009765625000]

                         The error in using 30 terms is

-0.9321439656095722205297890085495627239992875449526374431902381797209569109\

                                        -93
    579189394223552631188652867565109 10