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 10' 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:

            (3 b + 2 m - 1)! (2 a + 2 m - b)! (2 b - a + 2 m)! (3 a + 2 m - 1)!
 M(R)/R   = -------------------------------------------------------------------
                   m! (3 b + 3 m - 1)! (a + b + m - 1)! (3 a + 3 m - 1)!

MA(R)   =

/  m - 1                       \ /    m                                       \
| --------'                    | | --------'                                  |
|'  |  |    i! (3 b + 3 i - 1)!| |'  |  |    (a + b + i - 1)! (3 a + 3 i - 1)!|
|   |  |    -------------------| |   |  |    ---------------------------------|
|   |  |      (3 b + 2 i - 1)! | |   |  |             (2 a + 2 i - b)!        |
|   |  |                       | |   |  |                                     |
\  i = 0                       / \  i = 1                                     /

     /  m - 1                                         \
     | --------'                                      |
     |'  |  |                      1                  |
     |   |  |    -------------------------------------|
     |   |  |    (2 b - a + 2 i - 1)! (3 a + 2 i + 2)!|
     |   |  |                                         |
     \  i = 0                                         /

                                      and

 MA(R)
 -----  =  (3 b + 2 m - 1)! (2 a - b)! (2 b - a + 2 m)! (3 a + 2 m - 1)!
   R
               /  m - 1                    \ /  m - 1                        \
               | --------'                 | | --------'                     |
               |'  |  |    (3 a + 2 i - 1)!| |'  |  |      (2 b - a + 2 i)!  |
               |   |  |    ----------------| |   |  |    --------------------|/
               |   |  |    (3 a + 2 i + 2)!| |   |  |    (2 b - a + 2 i - 1)!|
               |   |  |                    | |   |  |                        |
               \  i = 0                    / \  i = 0                        /

               (m! (3 b + 3 m - 1)! (a + b - 1)! (3 a - 1)!)

              M(R)        (2 a + 2 m - b) (2 b - a + 2 m) (a + b + m)
          -----------  =  -------------------------------------------
                 MR                (3 b + 2 m) (3 a + 2 m) m
          R ABM(----)
                  R

                                      and

                   MA(R)          (2 a - b) (a + b) (- 2 b + a)
                -----------  =  - -----------------------------
                     MA(R)          (3 b + 2 m) (3 a + 2 m) m
                R BM(-----)
                       R

                                    Finally,

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