The result in question [5, p. 512, eq.(c),] is
The two methods now diverge completely. The WZ method produces a second order recurrence for , namelyand proves it by showing that if then
Identity (3.2) then follows by summing (3.4) from r=0 to r=m+2 (i.e. Zeilberger's creative telescoping .
This, of course provides a perfectly valid proof of (3.1); however we note the inability of the WZ method to establish directlyThe Pfaff method, on the other hand, cannot handle (3.1) by itself. It must simultaneously prove that [3, p. 2, eq.(2.3),] Pfaff's method proceeds now as in Section 2. Here we find directly [2, ,] and Pfaff's method then concludes by the observation that the right-hand sides of (3.1) and (3.6) also satisfy (3.7) and (3.8).