To get the Apery magical accelerating polynomial for Zeta(2)

                           type: AperyB(n^2,n,h,2);

                               and you would get

                                      2              2
                         - 1/2 - n - n  + n h - 1/2 h

         To get the Apery magical accelerating polynomial for Zeta(3)

                           type: AperyB(n^3,n,h,3);

                               and you would get

                        2    3        2          2      2    3
                  -n - n  - n  + 2 h n  + h - 2 h  n + h  + h

              To get the best rational function correction to the

           partial sum of the defining series for Catalan's constant

                  with degree of denomiator equalling 6, type:

                          RatAppx(-(2*n-1)^2,-1,n,6);

                                You would get:

                                             2         4
                             n (4237 + 9080 n  + 2640 n )
                   - 7/15 ----------------------------------
                                6               2          4
                          4928 n  + 375 + 9212 n  + 17360 n

              To get the best rational function correction to the

                 partial sum of the defining series for Zeta(5)

                  with degree of denomiator equalling 6, type:

                              RatAppx(n^5,1,n,6);

                                You would get:

                                                  2
                               983 + 264 n + 264 n
        1/6 -----------------------------------------------------------
                 6                       2         3         4        5
            176 n  + 107 + 864 n + 1754 n  + 1956 n  + 1418 n  + 528 n

        To see if there any hope for an Apery-style irrationality proof

                               for Zeta(2) type:

                             DeltaSeq(n^2,1,n,20);

                               and you would get:

[.969913, .550465, 1.05297, .437799, .525403, .400237, .333582, .297202,

    .789715, .284618, .399794, .282088, .318333, .259885, .399121, .255689,

    .212694, .163025, .196602]



                  Since they are all positive, there is hope!



        To see if there any hope for an Apery-style irrationality proof

                               for Zeta(3) type:

                         DeltaSeq1(n^3,1,n,14,Zeta(3));

                               and you would get:

[.259751, .321749, .0408495, .307571, .00780950, .0637536, .000503994, .232280,

    .0592976, .135248, .00183122, .0658182, .00436816, .0887921]


                  Since they are all positive, there is hope!



        To see if there any hope for an Apery-style irrationality proof

                          for Zeta(5) type:

                         DeltaSeq1(n^5,1,n,20,Zeta(5));

                               and you would get:

[-.377729, -.255966, -.383765, -.336846, -.385305, -.349812, -.426851, -.419374,

    -.474511, -.488432, -.477051, -.508854, -.541555, -.536735, -.558243,

    -.537418]

                   Since they are negative, there is NO hope!