For a specified (m, l)-fold hypergeometric term  in n and k, the KoepfZeilberger(T, n, k, En) command constructs for  a Z-pair  that consists of a linear difference operator with coefficients that are polynomials of n over the complex number field

and a function  such that

A function  is an (m, l)-fold hypergeometric term if  and  are rational functions of n and k.

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

Koepf, W. "Algorithms for m-fold Hypergeometric Summation." Journal of Symbolic Computation. Vol. 20 No. 4. (1995): 399-417.

Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, 1998.