This file finds recurrences for the integral, from 0 to 1 of powers of the C\
    hebyshev polynomials



                    ---------------------------------------



                                    1
                                   /
                                  |
    For the sequence defined by,  |   CHEBYSHEVfirstKind[n](x) dx, we have
                                  |
                                 /
                                   0



                                                                      2
                      (n + 2) (n - 1)     n (n + 3) N      n (n + 3) N       3
[[1/2, -1/3, -1/2], - --------------- + --------------- - --------------- + N ]
                      (n + 4) (n + 1)   (n + 4) (n + 1)   (n + 4) (n + 1)



                             and in Maple notation



                                                                      2
                      (n + 2) (n - 1)     n (n + 3) N      n (n + 3) N       3
[[1/2, -1/3, -1/2], - --------------- + --------------- - --------------- + N ]
                      (n + 4) (n + 1)   (n + 4) (n + 1)   (n + 4) (n + 1)



                    ---------------------------------------



                                    1
                                   /
                                  |                           2
    For the sequence defined by,  |   CHEBYSHEVfirstKind[n](x)  dx, we have
                                  |
                                 /
                                   0



                                 2 n - 1   4 (n + 1) N    2
                   [[1/3, 7/15], ------- - ----------- + N ]
                                 2 n + 5     2 n + 5



                             and in Maple notation



                                 2 n - 1   4 (n + 1) N    2
                   [[1/3, 7/15], ------- - ----------- + N ]
                                 2 n + 5     2 n + 5



                    ---------------------------------------



                                    1
                                   /
                                  |                           3
    For the sequence defined by,  |   CHEBYSHEVfirstKind[n](x)  dx, we have
                                  |
                                 /
                                   0



                                                      3        2
       -9  -7  -37   (n - 1) (3 n - 1) (3 n + 1) (57 n  + 425 n  + 1006 n + 748)
[[1/4, --, --, ---], -----------------------------------------------------------
       35  20  715                (3 n + 11) (3 n + 13) (n + 5) %1

                                        3
       114 n (3 n + 4) (3 n + 2) (n + 3)  N
     - ------------------------------------
         (3 n + 11) (3 n + 13) (n + 5) %1

                                  4        3         2                  2
       2 (3 n + 5) (3 n + 7) (57 n  + 456 n  + 1285 n  + 1492 n + 496) N
     + ------------------------------------------------------------------
                        (3 n + 11) (3 n + 13) (n + 5) %1

                                               3  3
       114 (3 n + 10) (n + 4) (3 n + 8) (n + 1)  N     4
     - -------------------------------------------- + N ]
             (3 n + 11) (3 n + 13) (n + 5) %1

          3        2
%1 := 57 n  + 259 n  + 342 n + 124



                             and in Maple notation



                                                      3        2
       -9  -7  -37   (n - 1) (3 n - 1) (3 n + 1) (57 n  + 425 n  + 1006 n + 748)
[[1/4, --, --, ---], -----------------------------------------------------------
       35  20  715                (3 n + 11) (3 n + 13) (n + 5) %1

                                        3
       114 n (3 n + 4) (3 n + 2) (n + 3)  N
     - ------------------------------------
         (3 n + 11) (3 n + 13) (n + 5) %1

                                  4        3         2                  2
       2 (3 n + 5) (3 n + 7) (57 n  + 456 n  + 1285 n  + 1492 n + 496) N
     + ------------------------------------------------------------------
                        (3 n + 11) (3 n + 13) (n + 5) %1

                                               3  3
       114 (3 n + 10) (n + 4) (3 n + 8) (n + 1)  N     4
     - -------------------------------------------- + N ]
             (3 n + 11) (3 n + 13) (n + 5) %1

          3        2
%1 := 57 n  + 259 n  + 342 n + 124



                    ---------------------------------------



                                    1
                                   /
                                  |                           4
    For the sequence defined by,  |   CHEBYSHEVfirstKind[n](x)  dx, we have
                                  |
                                 /
                                   0



                                                2
       107   (4 n - 1) (2 n - 1) (4 n + 1) (24 n  + 73 n + 54)
[[1/5, ---], -------------------------------------------------
       315            n (2 n + 5) (4 n + 7) (4 n + 9)

                                  3       2
       2 (4 n + 5) (4 n + 3) (24 n  + 14 n  - 28 n + 9) N    2
     - -------------------------------------------------- + N ]
                n (2 n + 5) (4 n + 7) (4 n + 9)



                             and in Maple notation



                                                2
       107   (4 n - 1) (2 n - 1) (4 n + 1) (24 n  + 73 n + 54)
[[1/5, ---], -------------------------------------------------
       315            n (2 n + 5) (4 n + 7) (4 n + 9)

                                  3       2
       2 (4 n + 5) (4 n + 3) (24 n  + 14 n  - 28 n + 9) N    2
     - -------------------------------------------------- + N ]
                n (2 n + 5) (4 n + 7) (4 n + 9)



                     --------------------------------------



                           This took, 4.533, seconds.