The Jackson table extension

Note:  x=cos(theta)
       w=exp(i*m*(phi)
 
For l=4: 

                  4         2        2               2 2        9
          w (384 x  + 1152 x  (-1 + x ) + 144 (-1 + x ) ) sqrt[----]
                                                               4 Pi
    Y40 = ----------------------------------------------------------
                                    384


                        2         3                 2          9
          -(w Sqrt[1 - x ] (3840 x  + 2880 x (-1 + x )) sqrt[-----])
                                                             80 Pi
    Y41 = ----------------------------------------------------------
                                    384


                  2          2               2          1
          w (1 - x ) (17280 x  + 2880 (-1 + x )) sqrt[------]
                                                      160 Pi
    Y42 = ---------------------------------------------------
                                    384 



                         2 3/2         1
    Y43 = -105 w x (1 - x )    sqrt[-------]
                                    2240 Pi
    



                      2 2         1
    Y44 = 105 w (1 - x )  sqrt[--------]
                               17920 Pi