Let A, B be forward and M be backward shift

                     operators on a, b and m respectively.

           Denote the identity on the right-hand-side of Thm 1' by R

             Then we verify that R(a,b,m) satisfies the recurrence



X(m - 1, a, b) X(m - 1, a + 1, b + 1) - X(m - 1, a + 1, b) X(m - 1, a, b + 1)
-----------------------------------------------------------------------------
                      X(m, a, b) X(m - 2, a + 1, b + 1)

     = 1,                                                                    or

                         M(R) MAB(R)   AM(R) BM(R)
                         ----------- - ----------- = 1
                          R MMAB(R)     R MMAB(R)

                                   Note that:

    M(R)
-----------  =
       MR
R ABM(----)
        R

      (m + a + b)        (2 a - b + 2 m)        (2 b - a + 2 m)
(1 + q           ) (1 - q               ) (1 - q               )

          (m + a + b)    /        (3 a + 2 m)        (3 b + 2 m)        (2 m)
    (1 - q           )  /  ((1 - q           ) (1 - q           ) (1 - q     ))
                       /

                                      and

   MA(R)
----------- = 
     MA(R)
R BM(-----)
       R

    (2 m)       (a + b + 2 m)        (2 a - b)        (2 b - a)        (a + b)
   q      (1 + q             ) (1 - q         ) (1 - q         ) (1 - q       )
   ----------------------------------------------------------------------------
                      (3 a + 2 m)        (3 b + 2 m)        (2 m)
                (1 - q           ) (1 - q           ) (1 - q     )

                                    Finally,

                            M(R)         MA(R)
                        ----------- - -----------  =  1
                               MR          MA(R)
                        R ABM(----)   R BM(-----)
                                R            R