Taylor Expansion of arctan(x)

               1                 a            2
arctan(a) = ------ (x - a) - --------- (x - a)
                 2                 2 2
            1 + a            (1 + a )

                           2
              1           a
         - ------ + 4 ---------
                2           2 2
           1 + a      (1 + a )         3
   + 1/3 ---------------------- (x - a)
                      2
                 1 + a

                                   2
               a         (- 1 + 3 a ) a
         2 --------- - 2 --------------
                 2 2              2 3
           (1 + a )         (1 + a )           4
   + 1/4 ------------------------------ (x - a)
                          2
                     1 + a

                    2      2         2
           - 1 + 3 a      a  (- 1 + a )
         - ---------- + 8 -------------
                  2 3             2 4
            (1 + a )        (1 + a )           5
   + 1/5 ------------------------------ (x - a)
                          2
                     1 + a

                     2               2      4
           a (- 1 + a )     (1 - 10 a  + 5 a ) a
         4 ------------ - 2 --------------------
                   2 4                  2 5
             (1 + a )             (1 + a )              6
   + 1/6 --------------------------------------- (x - a)
                               2
                          1 + a

                   2      4      2         4       2
           1 - 10 a  + 5 a      a  (3 + 3 a  - 10 a )
         - ---------------- + 4 ---------------------
                     2 5                    2 6
               (1 + a )               (1 + a )               7
   + 1/7 -------------------------------------------- (x - a)
                                 2
                            1 + a

                     4       2                 2       4      6
           a (3 + 3 a  - 10 a )     (- 1 + 21 a  - 35 a  + 7 a ) a
         2 -------------------- - 2 ------------------------------
                       2 6                           2 7
                 (1 + a )                      (1 + a )                   8
   + 1/8 --------------------------------------------------------- (x - a)
                                        2
                                   1 + a

                     2       4      6       2           2      4    6
           - 1 + 21 a  - 35 a  + 7 a       a  (- 1 + 7 a  - 7 a  + a )
         - -------------------------- + 16 ---------------------------
                          2 7                             2 8
                    (1 + a )                        (1 + a )                  9
   + 1/9 ------------------------------------------------------------- (x - a)
                                          2
                                     1 + a

              10
   + O((x - a)  )