For a specified q-hypergeometric term  of  and , the Zeilberger(T, n, k, q, Qn) calling sequence constructs for  a Z-pair  that consists of a linear q-difference operator with coefficients that are polynomials of

and a q-hypergeometric term  of  and  such that

Qn is the q-shift operator with respect to , defined by .

By assigning values to the global variables _MINORDER and _MAXORDER, the algorithm is restricted to finding a Z-pair  for  such that the order of L is between _MINORDER and _MAXORDER (the default value of _MAXORDER is 6).

The output from the Zeilberger command is a list of two elements  representing the computed Z-pair .

Petkovsek, M.; Wilf, H.; and Zeilberger, D. A=B. Wellesley, Massachusetts: A K Peters, Ltd., 1996.